“This short note is a validation of a previous work which found no correlation between changes in atmospheric CO2 and fossil fuel emissions at an annual time scale. In this work, this result is tested for robustness with respect to sample period selection within a range of data availability. A resampling procedure similar to bootstrap is used. Resampling ensures that the failure to find a correlation is not an artifact of the sample period chosen. The results validate the robustness of the previous finding and imply that there is no evidence that atmospheric CO2 is responsive to fossil fuel emissions at an annual time scale net of long term trends. This result is robust. It holds for all possible combination of years in the study period 1958-2015 1 .”
~ RESPONSIVENESS OF ATMOSPHERIC CO2 TO FOSSIL FUEL EMISSIONS: PART 2, by Professor Jamal Munshi.
budbromley 
Reblogged this on Climate- Science.press.
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Thus of the three relationships cited by climate science as empirical evidence for AGW, we are able to verify only one – that atmospheric CO2 and surface temperature are correlated at an annual time scale. This relationship alone, without evidence that changes in atmospheric CO2 derive from fossil fuel emissions, does not support the theory of AGW.
Bud, for the millions inept in statistics, can you explain the No correlation of fossil fuels and atmospheric CO2? I mean can you explain it in terms we non-statisticians can understand?
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Thank you for reading and thanks for your question.
Establishing that a correlation holds robustly for annual time periods, as compared to for example 200 years or 1000 year time periods, is important because then we can use current, measured data without resorting to long term data such as ice cores, tree rings etc which by their nature contain uncertainties and assumptions. In other words, we can validate or invalidate AGW with short term, measured data; it is not necessary to use long term data if the bias due to certain variables is removed.
Professor Munshi is not making any measurements in the field. He is using standard statistical tools to test data files published by other scientists. Trends, anomalies, weakness and strength are revealed with the tools, that is by mathematically interrogating the data files with well understood algorithms or data. Using these tools, he detrends the data, that is, he removes the effects on the data of seasons, drift in the data, which might be due to changes in the orbit of an aging measuring satellite, and other recurring trends. He interrogates the data to determine if the correlation is significantly affected by both the time period studied and the location of the sampling. He finds that sampling location is critical, as it changes the results. In other words, the bias introduced in climate data by using multiple sample locations must be removed.
The additional uncertainty introduced in the data by changing the sampling points requires extending the time period of the sampling in order to obtain statistically valid results. On the other hand, if the sampling points are held consistent, then the correlation is valid for one year periods.
Note that in this paper Professor Munshi is studying the correlation between the log of the CO2 concentration versus surface temperature. However, in this study he is not determining cause and effect, or the sequence in time of those two variables. He does that in a different study. If the correlation itself is not statistically robust without regard to timing, then any cause and effect implication would be invalid.
Professor Munshi reminds us, “Of course, even detrended correlation between field data do not serve as evidence of causation but such a correlation is still a necessary pre-condition to causation because no causation theory is possible in its absence (Wright, 1921) (McArthur, 1980).” In other words, the hypothesis proposed by AGW proponents is that an increasing CO2 concentration trend is causing a trend of increasing temperature, but a correlation between those two variables does not prove a cause and effect relationship exists. He tested what is known in science, math and statistics as the null hypothesis, which in AGW is, IF there is no correlation between the two variables, then a cause and effect relationship does not exist; he fails to falsify that null hypothesis. .
He uses a very demanding statistical technique to interrogate the data files. The technique is also published by others. It greatly reduces the possibility of a false positive result to the point of statistical improbability. His result shows that there is strong support that there is a causal relationship between those two variables.
Professor Munshi study here does not test or reveal which variable is the cause and which is the effect. “In the case of the data presented here the observed correlation is consistent with two alternative views – that atmospheric CO2 causes warming and that warming causes atmospheric CO2 to rise.” … or even a third or additional variables are not excluded from possibility.
He makes two very important takeaway points. (1) If certain biases are correctly removed from the data, for example sampling location, then time periods of one year are enough for statistically valid correlation, and (2) there is a significant correlation between the log of CO2 concentration and surface temperature.
Munshi, Salby, Dockery and others explore the details of this correlation further in other publications. Among other findings, they independently conclude that surface temperature trend is causing the trend in total CO2 concentration and separately that the 300% increase in reported atmospheric CO2 concentration resulting from human use of fossil fuels since year 2000 has had no significant or even measureable effect on the overall growth trend of CO2 concentration. In other words, human-contributed CO2 from fossil fuels is not significant and negligible with regard to earth’s surface temperature.
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