Correlation Analysis: CO2 Lags Temp! (a reblog)

Posted by: chaamjamal on: September 4, 2019

bandicam 2019-09-04 19-40-40-007



Humlum, Ole, Kjell Stordahl, and Jan-Erik Solheim. “The phase relation between atmospheric carbon dioxide and global temperature.” Global and Planetary Change 100 (2013): 51-69. 

Abstract: Using data series on atmospheric carbon dioxide and global temperatures we investigate the phase relation (leads/lags) between these for the period January 1980 to December 2011. Ice cores show atmospheric CO2 variations to lag behind atmospheric temperature changes on a century to millennium scale, but modern temperature is expected to lag changes in atmospheric CO2, as the atmospheric temperature increase since about 1975 generally is assumed to be caused by the modern increase in CO2. In our analysis we use eight well-known datasets: 1) globally averaged well-mixed marine boundary layer CO2 data, 2) HadCRUT3 surface air temperature data, 3) GISS surface air temperature data, 4) NCDC surface air temperature data, 5) HadSST2 sea surface data, 6) UAH lower troposphere temperature data series, 7) CDIAC data on release of anthropogene CO2, and 8) GWP data on volcanic eruptions. Annual cycles are present in all datasets except 7) and 8), and to remove the influence of these we analyze 12-month averaged data. We find a high degree of co-variation between all data series except 7) and 8), but with changes in CO2 always lagging changes in temperature. The maximum positive correlation between CO2 and temperature is found for CO2 lagging 11–12 months in relation to global sea surface temperature, 9.5–10 months to global surface air temperature, and about 9 months to global lower troposphere temperature. The correlation between changes in ocean temperatures and atmospheric CO2 is high, but do not explain all observed changes. ► Changes in global atmospheric CO2 are lagging 11–12 months behind changes in global sea surface temperature. ► Changes in global atmospheric CO2 are lagging 9.5–10 months behind changes in global air surface temperature. ► Changes in global atmospheric CO2 are lagging about 9 months behind changes in global lower troposphere temperature. ► Changes in ocean temperatures explain a substantial part of the observed changes in atmospheric CO2 since January 1980. ► Changes in atmospheric CO2 are not tracking changes in human emissions.





  1. The correlations claimed by the authors of the paper are tested with UAH satellite data for monthly mean lower troposphere temperatures 1979 to 2018 against Mauna Loa monthly mean CO2 data 1977 to 2018. Twenty four regional temperatures are tested. They are labeled numerically in the charts above as 1 to 24. They are, in sequence from 1 to 24, Global, G land, G ocean, Northern Hemisphere, NH land, NH ocean, Southern Hemisphere, SH land, SH ocean, Tropics, T land, T ocean, Northern Extent, NE land, NE ocean, Southern Extent, SE land, SE ocean, North Polar, NP land, NP ocean, South Polar, SP land, SP ocean. Both 12-month and 9-month lags are tested.
  2. Correlation and detrended correlation between temperature and lagged CO2 are computed and the results are summarized in the charts above. Figure 1 and Figure 3 show correlations between the source data at 12-month and 9-month lags. At both lags we find a large range of correlations from negative values to very high correlations of max-ρ=[0.787,0.811] with medians of median-ρ=[0.695,0.658] for 12-month and 9-month lag respectively. These correlations are statistically significant and appear to support the authors claim of a lagged correlation between atmospheric CO2 and surface temperature indicating that temperature rises first and CO2 follows 9-12 months later and that therefore it is not possible for atmospheric CO2 to be the causal agent of the observed warming.
  3. However, as described in related posts, correlations between two time series where both series have long term trends, can be driven by the trends and not by responsiveness at any finite time scale less than the full span of the data [LINK] . Detrended correlation is used to remove the spurious shared trend effect so that responsiveness of atmospheric CO2 to temperature can be tested. These detrended correlations are shown in Figure 2 and Figure 4. The charts show near zero detrended correlations of median-ρ=[0.011,0.009] for 12-month and 9-month lag respectively. Virtually none of the source data correlation survives into the detrended series. This result implies that the correlations seen in the source data are spurious and that the relationship they imply is illusory. Their only information content is that both series have a rising trend. No responsiveness at an annual time scale is found.
  4. CONCLUSION: The lagged correlation between surface temperature and atmospheric carbon dioxide concentration reported by these authors is spurious. Therefore the apparent responsiveness of atmospheric CO2 to surface temperature is illusory. In the absence of such responsiveness it cannot be claimed that the data presented show a reverse relationship between temperature and atmospheric carbon dioxide such that temperature drives carbon dioxide and not the other way around. 

Original blog post:

Reference linked in the above article: Spurious Correlations in Climate Science

Posted by: chaamjamal on: May 27, 2018

  1. DETRENDED CORRELATION ANALYSIS OF TIME SERIES DATA: Correlation between  x and y in time series data derive from responsiveness of y to x at the time scale of interest and also from shared long term trends. These two effects can be separated by detrending both time series as explained by Alex Tolley in the video frame of Figure 3. When the trend effect is removed only the responsiveness of y to x remains. This is why detrended correlation is a better measure of responsiveness than source data correlation as explained very well by Alex Tolley in the video. The full video may be viewed on Youtube [LINK] . That spurious correlations can be found in time series data when detrended analysis is not used is demonstrated with examples at the Tyler Vigen Spurious Correlation website [LINK] . Spurious correlations are common in climate science where many critical relationships that support the fundamentals of anthropogenic global warming (AGW) are found to  be based on spurious correlations.

The reader is strongly encouraged to read the full articles including the examples in the links.

About budbromley

Bud is a retired life sciences executive. Bud's entrepreneurial leadership exceeded three decades. He was the senior business development, marketing and sales executive at four public corporations, each company a supplier of analytical and life sciences instrumentation, software, consumables and service. Prior to those positions, his 19 year career in Hewlett-Packard Company's Analytical Products Group included worldwide sales and marketing responsibility for Bioscience Products, Global Accounts and the International Olympic Committee, as well as international management assignments based in Japan and Latin America. Bud has visited and worked in more than 65 countries and lived and worked in 3 countries.
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2 Responses to Correlation Analysis: CO2 Lags Temp! (a reblog)

  1. Bob King says:

    Dear Bud,
    I enjoy receiving your emails.
    Regarding the correlation analysis article, I wish to say that something just does not ring true, regarding paragraphs 3 and 4.
    If you had two perfectly correlated series, and then you removed the correlation, you would be left with a series of points along a flat line.
    If the two series were perfectly correlated and were also perfectly correlated in a perfect trend, once the trend was removed (or detrended), you would again be left with a series of points along a flat line.
    All you have done is proved the corrrelation.
    If the series were not perfectly correlated so that you are left with residuals, which in this article are stated to be uncorrelated, it means that your correlation has picked up all the information it can.
    Personally, I do not think this is a good article. It is simply a circular arguement.


    Bob King


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