THIS POST IS A PRESENTATION OF A RELATED WORK PUBLISHED AT SSRN.COM

LINK TO SOURCE: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2997420

A FOUNDATIONAL RELATIONSHIP IN THE THEORY OF ANTHROPOGENIC GLOBAL WARMING (AGW) IS THAT ATMOSPHERIC CO2 CONCENTRATION IS RESPONSIVE TO FOSSIL FUEL EMISSIONS AT AN ANNUAL TIME SCALE. THE RELATED WORK LINKED ABOVE IS A STATISTICAL TEST OF THIS HYPOTHESIS. THE ESSENTIAL FINDING IS THAT DETRENDED CORRELATION ANALYSIS FAILS TO PROVIDE EMPIRICAL EVIDENCE FOR THIS RELATIONSHIP. NO EVIDENCE IS FOUND THAT ATMOSPHERIC CO2 CONCENTRATION IS RESPONSIVE TO FOSSIL FUEL EMISSIONS AT AN ANNUAL TIME SCALE. WE CONCLUDE THAT THE FOUNDATIONAL ASSUMPTION OF AGW THEORY THAT FOSSIL FUEL EMISSIONS CHANGE ATMOSPHERIC COMPOSITION IS NOT SUPPORTED BY THE DATA.

THE RELEVANT SECTIONS OF THE SSRN PAPER ARE PROVIDED BELOW. THE FULL TEXT MAY BE FOUND AT THE LINK PROVIDED ABOVE.

PART-1: INTRODUCTORY COMMENTS

The essence of the theory of anthropogenic global warming (AGW) is that fossil fuel emissions cause warming by increasing atmospheric CO2 levels and that therefore the amount of warming can be attenuated by reducing fossil fuel emissions (Hansen, 1981) (Meinshausen, 2009) (Stocker, 2013) (Callendar, 1938) (Revelle, 1957) (Lacis, 2010) (Hansen, 2016) (IPCC, 2000) (IPCC, 2014). At the root of the proposed AGW causation chain is the ability of fossil fuel emissions to cause measurable changes in atmospheric CO2 levels in excess of natural variability. Evidence for this relationship between emissions and atmospheric CO2 has been presented in terms of carbon dioxide flows derived from climate models (Sarmiento, 1998) (Canadell, 2007) (Bachelet, 2001) (Friedlingstein, 2006) (McGuire, 2001) (Bopp, 2002) (Chen, 2000) and also from global carbon budgets based on the assessment of “net flows”. Net flows are differences between large uncertain flows but with the uncertainty removed by making certain assumptions. Net flows thus circumvent insurmountable measurement problems of large and uncertain gross flows (Massman, 2002) (Aubinet, 2012) (Rosón, 2003) (Giering, 2014) (Smith, 2001) (Lundberg, 1996) (Peltoniemi, 2006) (Ito, 2005) (Haverd, 2013) (Shvidenko, 1996) (Dufrêne, 2005). Net flows and flow information derived from climate models are a form of circular reasoning if they subsume AGW in the process of providing empirical evidence for AGW (Munshi, 2016) (Rodhe, 2000) (Edwards, 1999) and in particular if uncertainty is not given due consideration (Munshi, 2015a). A testable implication of the validity of a carbon budget constructed with net flow assumptions is its core AGW conclusion that changes in atmospheric CO2 are driven by fossil fuel emissions. Measurements of atmospheric CO2 at Mauna Loa 1958-2016 and worldwide 1967-2015 are used to carry out the test. In a prior study it was shown with Mauna Loa insitu CO2 data 1958-2011 that detrended correlation analysis does not provide evidence that changes in atmospheric CO2 are driven by fossil fuel emissions at an annual time scale (Munshi, 2015). This study is an update of the 2015 paper with extended data availability to 2016 as well as availability of global CO2 measurements.

PART-2: THE DATA

Weekly mean insitu atmospheric CO2 concentrations in parts per million measured at the Mauna Loa
1958-2016 are provided by the Scripps CO2 Program of UC San Diego (Scripps CO2 Program, 2017). Discrete flask measurements of atmospheric CO2 from 104 stations around the world are provided by the Earth System Research Laboratory of the NOAA for various sample periods within the range of 1967-2015 (ESRL, 2017). Twenty three of these stations are selected for this study using a criterion of at least 20 years of data availability. The selected stations, listed in Figure 2, provide a wide geographical distribution. They include Mauna Loa as well as stations in the South Pole, Australia, Canada, Alaska, the lower 48 states of the USA, the South Pacific, China, Central Asia, Europe, and Russia and provide more than 102,500 discrete flask atmospheric CO2 measurements for the period 1967- Figure 1 shows that data availability is sparse prior to 1981 in the ESRL dataset and that atmospheric CO2 rose from about 320 ppm in 1967 to more than 400 ppm in 2015. Data availability is more uniform in the Scripps insitu weekly mean data and they also show rising CO2 levels in the atmosphere from less than 320 ppm in 1958 to more than 400 ppm in 2016. Because of the difference in data availability between the early years and later years in the ESRL data, and also because it is helpful to test the robustness of results with respect to sample period, both datasets are studied for different time spans. The full span of the data for both datasets and the period 1981 to 2015, a period with good data availability that is common to both datasets, are studied. An annual time scale is used as is usual in the study of the impact of emissions on atmospheric CO2 (Bousquet, 2000) (Canadell, 2007) (Gillett, 2013). For the NOAA/ESRL data, a single amalgamated time series of all 102,517 measurements from all twenty three stations is created and the mean and standard deviation of atmospheric CO2 for each year of data are derived and used in a Monte Carlo procedure to simulate the uncertainty in the data. Annual changes in atmospheric CO2 are computed as the corresponding difference in parts per million reported by the measuring stations multiplied by 2.12 to convert ppm to gigatons of carbon equivalent (GTC). Data for fossil fuel emissions in millions of tons of carbon equivalent are provided by the Carbon Dioxide Information Analysis Center of the Oak Ridge National Laboratories (CDIAC, 2017). Data are available from 1750 to 2013 provided as megatons of carbon equivalent per year. These values are divided by 1000 and reported in this work as gigatons of carbon equivalent per year (GTC). Emissions for later years are inferred from percentage changes reported by other sources (CarbonBrief, 2016) (The Conversation, 2016) (Netherlands Environmental Assessment Agency, 2016).

PART-3: METHOD

Correlation between annual changes in atmospheric CO2 and the corresponding fossil fuel emissions are computed both in the source time series and in the detrended series. Uncertainty in the data causes the computed correlations to be somewhat different from one simulation to the next. Ten consecutive simulations are used as a representative sample of the correlation. The standard deviation of correlation is estimated using Bowley’s procedure (Bowley, 1928). Correlation in the source time series can be spurious because it contains both the time scale effect being investigated and an effect of a common drift in time in the two series. For this reason both time series must be detrended to isolate the effect at any given time scale (Podobnik, 2008) (Hu, 2001) (Munshi, 2016). Both source data correlation and detrended correlation are reported and tested for statistical significance. There are three combinations of source and detrended correlations, viz, (1) the source data are correlated and the correlation survives into the detrended series, (2) the source data are correlated but the correlation does not survive into the detrended series, and (3) the source data are not correlated. Only case (1) provides evidence of correlation at the time scale being studied. Case (2) indicates that the correlation in the source data derive mostly from a shared long term drift in time and not at the time scale being studied. Because a positive correlation is necessary to establish the causal relationship between changes in atmospheric CO2 and fossil fuel emissions described in the IPCC carbon budget, statistical significance is established with the one tailed hypothesis test H0: ρ≤0 against HA: ρ>0. Here ρ represents the correlation in the underlying phenomenon that generated the sample data being studied. The maximum false positive error rate is set to α=0.001, much lower than the usual values of α=0.01 to α=05, in accordance with Revised Standards for Statistical Significance (Johnson, 2013) published by the NAS to address an unacceptable rate of irreproducible results in published research (Siegfried, 2010). Since ten comparisons are made for the ten different simulation results for each correlation tested, the probability of finding at least one significant correlation in random data is increased by a factor of ten (Holm, 1979). The maximum false positive error rate is maintained by the requiring multiple rejections of H0 in any given set of ten comparisons rather than applying the so called Bonferroni Adjustment N(Armstrong, 2014) (Moran, 2003) (Garamszegi, 2006). For the annual time scale, emissions is set to EJ for the Jth year and atmospheric accumulation is computed as 2.12*(CJ-CJ-1). Here EJ is fossil fuel and cement emissions in gigatons of carbon equivalent in the Jth year and CJ is average atmospheric CO2 concentration for the Jth year denoted in parts per million. This work represents an update and further study of the relationship between fossil fuel (and cement production) emissions and atmospheric accumulation of carbon dioxide presented in prior studies (Munshi, Responsiveness of Atmospheric CO2 to Anthropogenic Emissions: A Note , 2015) (Munshi, Responsiveness of Atmospheric CO2 to Fossil Fuel Emissions: Part 2, 2016) (Munshi, Some Methodological Issues in Climate Science, 2016). All data and computational details used in this study are available in an online data archive (Munshi, 2017 Atmospheric CO2 paper Data Archive, 2017).

PART-4: DATA ANALYSIS

Annual means of the weekly mean insitu atmospheric CO2 data provided by Scripps are tabulated in Figure 3. The listed variables are MEAN = annual mean of the reported atmospheric carbon dioxide values, STDEV = their standard deviation, N = number of values reported that year, SE = the standard error of the mean, SIM-MEAN = Monte Carlo simulation of the mean that captures uncertainty implied by the standard error, EMISSIONS = fossil fuel and cement carbon dioxide emissions reported as gigatons of carbon equivalent per year (GTC), SIM-INCREASE = annual accumulation of CO2 in the atmosphere computed from the SIM-MEAN column as this year’s CO2 level minus previous year’s CO2 level and converted to GTC, DETEMIS = detrended emissions, and DETINCR = detrended annual CO2 accumulation. Values in the two SIM columns will be different for each simulation. Ten different Monte Carlo simulations are used and the correlation between SIM-INCR and EMISSIONS and that between DETINCR and DETEMIS are computed for each simulation and tested for statistical significance at α=0.001 per comparison. Results for the time span of 1958-2016 and time scale of one year are tabulated in Figure 4 where CORR refers to the correlation between the source data (SIM-INCREASE and EMISSIONS) and DETCORR to the detrended correlation between DETINCR and DETEMIS. The eleven rows in the Table represent eleven different simulations.

The CORR columns in Figure 4 show strong statistically significant correlations for the source data in all eleven simulations. The simulations capture the uncertainty in annual mean CO2 accumulation. The null hypothesis H0: ρ≤0 is rejected in all eleven simulations. At the same time the DETCORR columns show a complete failure to reject H0 for detrended correlations. A graphical representation of these results appears in Figure 5. The combination of a correlation in the source data and absence of correlation at a given time scale in the detrended series indicates that the correlation in the source data derives from a shared long term drift in time and not from a relationship between their annual fluctuations net of long term trend. These results show that the data do not provide evidence that EMISSIONS and SIM-INCREASE are related at an annual time scale. This result is consistent with the findings in prior works (Munshi, 2015) and inconsistent with the IPCC carbon budget and the AGW hypothesis which assume that observed increases in atmospheric CO2 derive from fossil fuel emissions (Le Quéré, 2009) (Canadell, 2007) (Solomon, 2009) (Hansen, 1981) (IPCC, 2000) (IPCC, 2014).

We now look at the same data for two additional time spans for ease of comparison with the dataset of global flask CO2 measurements. Figures 6&7 summarize the results for the time span 1967-2015 and Figures 8&9 show results for the span 1981-2015. The time scale is annual in both cases. The time for emissions to become well mixed in the atmosphere is thought to be one year (Bousquet, 2000).

For the span 1967-2015 (Figures 6&7), strong evidence of correlation is found in the source data but no correlation can be detected in the detrended series. As we did for the full span 1958-2015, we conclude that correlation in the source data derives from long term trends and not from correspondence in year to year fluctuations. Somewhat different results are seen for the span 1981-2015 (Figures 8&9). No statistically significant correlation is found in the detrended series or in the source data. These data also fail to provide evidence in support of the IPCC carbon budget that relates changes in atmospheric CO2 to fossil fuel emissions at an annual time scale.

PART-5: 2017 UPDATE

The results of detrended correlation analysis of global flask CO2 measurements for the full span of the data 1967-2015 are summarized in Figures 11&12. As in Figures 8&9, we find that although the correlation in the source data appears to be higher than that in the detrended series, no statistically significant correlation is found in either series at the maximum false positive error rate of α=0.001 per comparison used in this study. However, for the shorter time span of 1981-2015 (Figures 13&14) where data availability is more uniform across the study period (Figure 1), the source data correlations are much higher and here we see the results similar to those depicted in Figures 4&5 (Mauna Loa 1958- 2016) and Figures 6&7 (Mauna Loa 1967-2015) with a strong correlations in the source data that goes away when the data are detrended.

In all of the above cases, the absence of correlation in the detrended series fails to provide empirical support for the usual carbon budget hypothesis that emissions drive changes in atmospheric CO2. In cases where the a correlation is found in the source data, its absence in the detrended series indicates that the source data correlation derives from a shared drift in time and not from shared fluctuations at the specified time scale that is prerequisite to a causation hypothesis (Podobnik, 2008) (Chatfield, 1989). These results are consistent with findings in prior works that also found no empirical evidence that changes in atmospheric CO2 are driven by fossil fuel emissions at an annual time scale (Munshi, 2015) (Munshi, 2016). All data and computational details are available in a data archive (Munshi, 2017).

PART-6: SUMMARY AND CONCLUSIONS

A key relationship in the theory of anthropogenic global warming (AGW) is that between annual fossil fuel emissions and annual changes in atmospheric CO2. The proposed causation sequence is that annual fossil fuel emissions cause annual changes in atmospheric CO2 which in turn intensifies the atmosphere’s heat trapping property. It is concluded that global warming is due to changes in atmospheric composition attributed to human activity and is therefore a human creation and that therefore we must reduce or eliminate fossil fuel emissions to avoid climate catastrophe (Parmesan, 2003) (Stern, 2007) (IPCC, 2014) (Flannery, 2006) (Allen, 2009) (Gillett, 2013) (Meinshausen, 2009) (Canadell, 2007) (Solomon, 2009) (Stocker, 2013) (Rogelj, 2016).

A testable implication of the proposed causation sequence is that annual changes in atmospheric CO2 must be related to annual fossil fuel emissions at an annual time scale. This work is a test of this hypothesis. We find that detrended correlation analysis of annual emissions and annual changes in atmospheric CO2 does not support the anthropogenic global warming hypothesis because no evidence is found that changes in atmospheric CO2 are related to fossil fuel emissions at an annual time scale. These results are consistent with prior works that found no evidence to relate the rate of warming to the rate of emissions (Munshi, The Correlation between Emissions and Warming in the CET, 2017) (Munshi, Long Term Temperature Trends in Daily Station Data: Australia, 2017) (Munshi, Generational Fossil Fuel Emissions and Generational Warming: A Note, 2016) (Munshi, Decadal Fossil Fuel Emissions and Decadal Warming: A Note, 2015) (Munshi, Effective Sample Size of the Cumulative Values of a Time Series, 2016) (Munshi, The Spuriousness of Correlations between Cumulative Values, 2016).

IT IS NOTED THAT CLIMATE SCIENCE HAS PROPOSED AN ALTERNATIVE THEORY THAT DOES NOT REQUIRE THE CORRELATION WE TESTED ABOVE. THE ALTERNATIVE THEORY, CALLED THE TCRE, HOLDS THAT GLOBAL MEAN SURFACE TEMPERATURE IS PROPORTIONAL TO CUMULATIVE EMISSIONS AND THEREFORE RESPONSIVNESS OF ATMOSPHERIC COMPOSITION TO EMISSIONS TESTED ABOVE IS NOT REQUIRED.

HOWEVER, THERE IS A SERIOUS FLAW IN THE TCRE IN TERMS OF A MATHEMATICAL INCONSISTENCY. THE THEORY OF THE GREENOUSE EFFECT OF CO2 IMPLIES THAT GLOBAL MEAN SURFACE TEMPERATURE (GMST) IS A LOGARITHMIC FUNCTION OF ATMOSPHERIC CO2 CONCENTRATION THAT DERIVES FROM CUMULATIVE EMISSIONS BUT THE NEW TCRE HOLDS THAT THE RELATIONSHIP IS NOT LOGARITHMIC BUT LINEAR. THIS INCONSISTENCY MAKES IT IMPOSSIBLE FOR THE TCRE AND THE GREENHOUSE EFFECT TO DESCRIBE THE SAME PHYSICAL PHENOMENON. THE MATHEMATICAL INCONSISTENCY ISSUE IS DESCRIBED IN A RELATED POST:

LINK: https://tambonthongchai.com/2020/08/26/a-mathematical-inconsistency/

THE OTHER PROBLEM WITH THE TCRE IS THAT A TIME SERIES OF THE CUMULATIVE VALUES OF ANOTHER TIME SERIES CONTAINS NEITHER TIME SCALE NOR DEGREES OF FREEDOM.

CITATIONS: AVAILABLE IN THE SOURCE DOCUMENT AT SSRN LINKED ABOVE