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Archive for the ‘global warming’ Category















  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.
  2. EXAMPLE 1:  For example, climate science assumes that changes in atmospheric CO2 concentration since pre-industrial times are due to fossil fuel emissions of the industrial economy. This attribution is supported by a strong correlation between the rate of emissions and the rate of increase in atmospheric CO2 concentration in the time series of the source data. However, when the two time series are detrended, the correlation is not found. This result of detrended correlation analysis implies that the correlation seen in the source data derives from shared trends and not from responsiveness at an annual time scale. Details of this test are presented in a related post  [LINK] .
  3. EXAMPLE 2: A similar relationship is found in the ocean acidification hypothesis which claims that changes in the inorganic carbon concentration of oceans are driven by fossil fuel emissions. There, too the source data do show a strong correlation but that correlation vanishes when the two time series are detrended. As before, this pattern implies that the correlation in the source data derives from shared trends and not from responsiveness at an annual time scale. [LINK] .
  4. EXAMPLE 3: It is claimed that the observed rise in atmospheric methane concentration is due to human caused methane emissions in activities such as cattle ranching and dairy farming as well as rice cultivation and oil and gas production. Here too, a strong correlation is found in the time series of the source data but this correlation does not survive into the detrended series. This result implies that the correlation between human caused methane emissions and the rise in atmospheric methane derives from shared trends and not from responsiveness at an annual time scale. Such responsiveness is a necessary, though not sufficient, condition for causation.  Details of this work may be found in a related post at this site [LINK] .
  5. EXAMPLE 4: A cornerstone of climate science is the effectiveness of proposed climate action in the form of reducing fossil fuel emissions. That the rate of warming can be attenuated by reducing fossil fuel emissions requires that the rate of warming must be responsive to the rate of emissions at the appropriate time scale for this causation to occur (thought to be a decade or perhaps longer (Ricke&Caldeira 2014). And in fact, we find a strong correlation between the rate of warming and the rate of emissions in the time series of the source data at five different time scales (10, 15, 20, 25, & 30 years). Both of these source time series show an upward trend such that the shared trend can create spurious correlations as in the Alex Tolley lecture. When the two time series are detrended, the correlation disappears. The absence of detrended correlation implies that the observed correlation was a faux relationship driven by shared trends and not by responsiveness at the time scales tested in the analysis as demonstrated in a related post [LINK] . Thus no evidence is found in the data that reducing emissions will slow down the rate of warming.
  6. EXAMPLE 5: It is also claimed in climate science that reducing emissions will slow down the rate of sea level rise. This relationship requires a responsiveness of the rate of sea level rise to the rate of emissions at the appropriate time scale for this causation. And in fact, we find a strong correlation between the rate of sea level rise and the rate of emissions in the time series of the source data at five different time scales ranging from 30 to 50 years. Both of these source time series show an upward trend such that the shared trend can create a faux correlation. When the two time series are detrended, the correlation disappears. The absence of detrended correlation implies that the observed correlation was a spurious relationship driven by shared trends and not by responsiveness at the time scales tested in the analysis. This work may be found in a related post [LINK] .
  7. EXAMPLE 6: Climate science supports the greenhouse gas heat trapping theory of atmospheric CO2 and the relevance of their climate models with a strong correlation between model projections of surface temperature and actual observations (see for example Santer 2019). However, this correlation is also between two time series with rising trends. In a related post it is shown that there is indeed a strong correlation between the source data but this correlation is not found in the detrended series [LINK]
  8. EXAMPLE 7: Arctic sea ice extent has played an important role in climate change fear based activism because of periods of diminishing summer minimum sea ice extent in September and the forecasts of “ice free Arctic” that these trends have engendered. The underlying fear of human caused climate change causing Arctic sea ice melt was thus created. The evidence for the causal connection for this causation is a correlation between the rate of warming and the rate of summer sea ice decline; but detrended correlation analysis shows that this correlation is spurious as no year to year responsiveness of September Arctic sea ice extent to the rate of warming is found in the detrended series [LINK] .
  9. EXAMPLE 8: With the assumption that the observed rise in atmospheric CO2 concentration is driven by fossil fuel emissions (discussed in example 1) the effect of higher atmospheric CO2 concentration on climate is then established in terms of climate sensitivity, that is the responsiveness of surface temperature to the logarithm of atmospheric CO2 concentration. The validity of the climate sensitivity function can be shown with strong and statistically significant correlations between the climate model temperature series and observations. However, as shown in a related post [LINK] , this correlation does not survive into the detrended series and is therefore a spurious correlation, similar to the Tyler Vigen examples, that derives from shared trends and not from responsiveness at an annual or other fixed and finite time scale.
  10. EXAMPLE 9: The theory of the greenhouse gas effect of atmospheric CO2 predicts that as the CO2 concentration rises, it will cause tropospheric temperatures to rise and at the same time will cause lower stratospheric temperatures to fall. Thus we expect that that the lower stratospheric temperature will be responsive to mid-tropospheric temperature at an annual time scale and climate scientists claim that this is exactly what we find in the observational data. The evidence presented is a strong correlation between tropospheric temperature and lower stratospheric temperature. However, detrended correlation shows that this correlation derives from shared trends and not from a responsiveness of lower stratospheric temperature to mid tropospheric temperature at an annual time scale. The details of this analysis is described in a related post  [LINK] .
  11. EXAMPLE 10:  An additional argument for the attribution of increases in atmospheric CO2 to fossil fuel emissions is presented by climate science in terms of the observed dilution of the 14C isotope fraction of carbon in atmospheric CO2. It is claimed that this dilution proves that fossil fuel emissions accumulate in the atmosphere because fossil fuel carbon is known to contain low or no 14C having been dead and underground for millions of years. A test of this hypothesis shows that the correlation presented by climate science as empirical evidence in support of this theory is spurious. Details in a related post [LINK] .
  12. MOVING AVERAGES AND OTHER PRE-PROCESSED TIME SERIES DATA. When moving averages or moving sums of a time series are used to construct a derived time series, care must be taken to correct for the effective sample size (EFFN) in hypothesis tests because multiplicity (the use of the same data point more than once) reduces the effective sample size. When the reduction in degrees of freedom is not taken into account faux statistical significance can lead to spurious findings . This issue is discussed in some detail in a related post [LINK] and an example of this statistical error in climate science is presented in another related post [LINK] .
  13. A TIME SERIES OF THE CUMULATIVE VALUES OF ANOTHER TIME SERIES: An extreme case of such multiplicity is the construction of a time series of the cumulative values of another time series. In these cases it can be shown that the effective sample size is always EFFN=2 so that the degrees of freedom in hypothesis tests is DF=0. This relationship is described in an online paper [LINK] with the relevant text reproduced in paragraph#8 below. It should also be noted that the time series of the cumulative values of another time series does not contain a time scale. Thus, without either time scale or degrees of freedom, it is not possible to test for the statistical significance of any statistic for a time series of the cumulative values of another time series. The spuriousness of such correlations is demonstrated with Monte Carlo simulation in paragraph#9 below.
  14. EFFECTIVE SAMPLE SIZE OF THE CUMULATIVE VALUES OF A TIME SERIES. If the summation starts at K=2, series cumulative values of a time series X of length N is computed as Σ(X1 to X2), Σ(X1 to X3), Σ(X1 to X4), Σ(X1 to X5) … Σ(X1 to XN-3), Σ(X1 to XN-2), Σ(X1 to XN-1), Σ(X1 to XN). In these N-K+1 cumulative values, XN is used once, XN-1 is used twice, XN-2 is used three times, XN-3 is used four times, X4 is used N-3 times, X3 is used N-2 times, X2 is used N-1 times , X1 is used N-1 times. In general, each of the first K data items will be used N-K+1 times. Thus, the sum of the multiples for the first K data items may be expressed as K*(N-K+1). The multiplicities of the remaining N-K data items form a sequence of integers from one to N-K and their sum is (N-K)*(N-K+1)/2. The average multiplicity of the N data items in the computation of cumulative values may be expressed as AVERAGE-MULTIPLE = [(K*(N-K+1) + (N-K)*(N-K+1)/2]/N. Since multiplicity of use reduces the effective value of the sample size we can express the effective sample size as: EffectiveN = N/(AVERAGE-MULTIPLE) = N2/(K*(N-K+1) + (N-K)*(N-K+1)/2). To be able to determine the statistical significance of the correlation coefficient it is necessary that the degrees of freedom (DF) computed as effectiveN -2 should be a positive integer. This condition is not possible for a sequence of cumulative values that begins with Σ(X1 to X2). Effective-N can be increased to values higher than two only by beginning the cumulative series at a later point K>2 in the time series so that the first summation is Σ(X1 to XK) where K>2. In that case, the total multiplicity is reduced and this reduction increases the value of effectiveN somewhat but not enough to reach values much greater than two.
  16. EXAMPLE 1: An example of the use of cumulative values in climate science is the so called TCRE or Transient Climate Response to Cumulative Emissions. It is the correlation between cumulative emissions and cumulative warming (note that temperature = cumulative warming). This relationship shows a nearly perfect proportionality that is thought to provide convincing evidence of a causal relationship between emissions and temperature and provides a convenient metric for the computation of the so called remaining “carbon budget”, that is the amount of additional emissions possible for a given constraint on the amount of warming. The spuriousness of the TCRE proportionality is described in a related post on this site [LINK] and its spuriousness is further supported with a parody of the procedure that shows that UFO visitations are the real cause of global warming [LINK] . A related post shows that when a finite time scale is inserted into the TCRE, the correlation disappears [LINK] .
  17. EXAMPLE 2: A paper by Peter Clark of Oregon State University extended the TCRE methodology to sea level rise to provide empirical evidence that fossil fuel emissions cause sea level rise and that climate action in the form of reducing fossil fuel emissions should moderate the rate of sea level rise. (Clark, Peter U., et al. “Sea-level commitment as a gauge for climate policy” Nature Climate Change 8.8 2018: 653). In a related post on this site it is shown that this correlation is spurious [LINK] . In another, we show that when finite time scales are inserted so that both time scale and degrees of freedom are available for carrying out hypothesis tests, the correlation seen in the cumulative series is not found [LINK] .
  18. EXAMPLE 3: It is claimed that a correlation between cumulative values provides evidence that the decay in atmospheric 13C/12C isotope ratio is related to fossil fuel emissions and proves that the observed increase in atmospheric CO2 is driven by fossil fuel emissions. This claim and spurious correlation are addressed in a related post [LINK] .
  19. EXAMPLE 4: Climate science claims that dilution of the 13C isotope of carbon in atmospheric CO2 provides evidence that the observed increase in atmospheric CO2 concentration is caused by fossil fuel emissions. A strong correlation is presented as evidence but the correlation is between cumulative values and therefore spurious. When that error is corrected, no correlation is found [LINK] .
  20. THE INTERPRETATION OF VARIANCE IN CLIMATE SCIENCE STATISTICS. A related issue in statistical analysis methods of climate scientists is the way variance is interpreted. In statistics and also in information theory, high variance implies low information content. In other words, the higher the variance the less we know. In this context high variance is undesirable because it degrades the information we can derive from the data. However, high variance also yields large confidence intervals making it possible for high variance to be interpreted not as absence of information but as information about a danger of how extreme it could be. This interpretation of variance is common in climate science. In conjunction with the precautionary principle, it leads to a perverse interpretation of uncertainty such that uncertainty about the mean becomes transformed into certainty of extreme values. For example if the mean value of empirical climate sensitivity is found to have no statistical significance because of a large variance over a range of λ=2 to λ=6, the conclusion drawn by climate science from these data is not that we don’t really know what the value of λ is or even whether this concept can be verified with empirical evidence, but an obsession with the high value of λ=6 along with the alarming fear of the highest possible value in a range that actually implies that we don’t know. This interpretation of variance is aided by the use of the precautionary principle which holds that if a possible value of something that is harmful is high it is better to take precaution against that possibility than to interpret the data in a strictly rational way. In other words, the less you know the more extreme it COULD be and this use of the word “could” is common in climate science in the use of ignorance in the form of high variance to create fear.
  21. THE USE OF CIRCULAR REASONING IN CLIMATE SCIENCE STATISTICS:  In carrying out the flow accounting of the carbon cycle as a way of determining the effect of carbon in fossil fuel emissions on the carbon cycle, climate science is faced with the impossibility of measuring the much larger flows of carbon to and from the atmosphere in the carbon cycle. This difficulty is overcome by using the time series of atmospheric CO2 concentration from the Mauna Loa observatory that shows atmospheric CO2 concentration rising over time. By attributing the changes in atmospheric CO2 to fossil fuel emissions, a flow account of the unmeasurable carbon cycle can be inferred. The inferred flow account is then used to determine that the observed rise in atmospheric CO2 concentration is explained in terms of fossil fuel emissions.  This issue is presented in detain in two related posts [LINK] [LINK] .







Posted on: May 2, 2016

4/15/2018:  The Charney Sensitivity of Homicides to Atmospheric CO2: A Parody

3/21/2018:  Extraterrestrial Forcing of Surface Temperature and Climate Change: A Parody

3/17/2018:  From Equilibrium Climate Sensitivity to Carbon Climate Response

2/14/2018: Uncertainty in Empirical Climate Sensitivity

8/272017: Effect of Fossil Fuel Emissions on Sea Level Rise

7/5/2017: Responsiveness of Atmospheric CO2 to Fossil Fuel Emissions 

7/12/2017: Limitations of the TCRE: Transient Climate Response to Cumulative Emissions

12/1/2016: Illusory Statistical Power in Time Series Analysis

11/21/2016: Some Methodological Issues in Climate Science

11/15/2016: Responsiveness of Polar Sea Ice Extent to Air Temperature 1979-2016

11/1/2016: Responsiveness of Atmospheric CO2 to Fossil Fuel Emissions: Part 2

10/30/2016: Unstable Correlations between Atmospheric CO2 and Surface Temperature

10/21/2016: The Acid Rain Program Part 1: Lake Acidity in the Adirondacks

10/16/2016: Effective Sample Size of the Cumulative Values of a Time Series

9/30/2016: Generational Fossil Fuel Emissions and Generational Warming: A Note

9/24/2016: The Trend Profile of Mean Global Total Column Ozone 1964-2009

9/15/2016: Trend Profiles of Atmospheric Temperature Time Series

08/22/2016: Spurious Correlations in Time Series Data

07/23/2016: SDG: Climate Activism Disguised As Development Assistance

06/13/2016: The United Nations: An Unconstrained Bureaucracy

5/18/206: Changes in the 13C/12C Ratio of Atmospheric CO2 1977-2014

5/16/2016: Shale Gas Production and Atmospheric Ethane

5/6/2016: The OLS Warming Trend at Nuuk, Greenland

4/30/2016: Dilution of Atmospheric Radiocarbon CO2 by Fossil Fuel Emissions

4/19/2016: The Hurst Exponent of Sunspot Counts

4/12/2016: Seasonality and Dependence in Daily Mean USCRN Temperature

4/1/2016: Mean Global Total Ozone from Ground Station Data: 1987-2015

3/15/2016: Latitudinally Weighted Mean Global Ozone 1979-2015

2/1/2016: The Spuriousness of Correlations between Cumulative Values

1/21/2016: An Empirical Test of the Chemical Theory of Ozone Depletion

11/2015: The Hurst Exponent of Precipitation

11/11/2015: The Hurst Exponent of Surface Temperature

10/14/2015: Responsiveness of Atmospheric Methane to Human Emissions

10/6/2016: An Empirical Study of Fossil Fuel Emissions and Ocean Acidification

9/19/2015: Decadal Fossil Fuel Emissions and Decadal Warming

9/1/2015: Uncertain Flow Accounting and the IPCC Carbon Budget

8/21/2015: Responsiveness of Atmospheric CO2 to Anthropogenic Emissions

7/15/2015: A Robust Test for OLS Trends in Daily Temperature Data

6/2015: A General Linear Model for Trends in Tropical Cyclone Activity

3/1/2015: Uncertainty in Radiocarbon Dating: A Numerical Approach

10/20/2014: Simulation as a Teaching Tool in Finance

6/25/2014: The Rise and Fall of the Arbitrage Pricing Theory

6/11/2014: There is No Chaos in Stock Markets

3/23/2014: The Hamada Equation Reconsidered

More: All papers at

SSU: Sonoma State University

The notion that our carbon dioxide emissions are causing the oceans to warm at an alarming rate making glaciers flow faster into the sea (Staying afloat in a sinking world, Bangkok Post, November 24, 2010) is logically and scientifically flawed in many ways. I would like to cite only one of them and it has to do with the Argo Project. It was launched with much fanfare about six years ago. Thousands of robotized floats were installed in oceans around the globe to measure “just how fast the ocean is warming”.  By their own reckoning, these measurements provide the most accurate and comprehensive sea temperature data available to them. Yet, mysteriously, the hype went out of the Argo Project almost as soon as it was implemented. Not only that, the Argo data are apparently being shunned by climate scientists who prefer the old measuring devices whose inadequacy was apparently the reason that they had sought funding for Argo. NASA’s JPL, the keepers of the Argo data, admitted that it is because there are no trends in the temperature or salinity data from the Argo floats. Had the data showed the kind of warming they had hoped to find, the media would have been inundated with that information. The fundamental bias in climate science is that data that do not support its presumptions are not considered valid.

Cha-am Jamal

During 2005 and 2006 the global warming press was abuzz with news about the Argo project – a global effort by climate scientists to cover the earth with thousands of robotized buoys to measure sea temperature. The new devices would aid global warming scientists to “gain new information on the heat trapped in the oceans” and “really track how the ocean is warming” (Sea robots aid climate research, ABC Online,, November 16, 2006).

The initial deployment of the measuring stations was completed in 2007 and more than 3 years have  now elapsed but we have not heard from the climate scientists about the new information they have found about how the oceans are trapping heat and warming. The line has gone dead. Could it be that they did not find what they had spent all the money and effort to find? It is clear from the language that the effort was not an unbiased study to discover whether the oceans were warming but only to confirm that it was warming and to hand skeptics a slam dunk but instead of silencing skeptics with the new data, climate scientists appear to have forgotten about the Argo Project and are now pushing land temperatures.

Cha-am Jamal

The so called “climate change vulnerability index”, that is likely causing great economic harm to countries like Bangladesh and India by implying that they pose higher risk to investors, is based on the proposition that “there is growing evidence that climate change is increasing the intensity and frequency” of weather related natural disasters. In fact there is no such evidence. This idea was included in the IPCC’s 2007 assessment report based on a peer reviewed research paper but that paper having been shown to be flawed, the IPCC has since made a full retraction of this claim (UN wrongly linked global warming to natural disasters, The Sunday Times, January 24, 2010). However, this orphaned idea has taken on a life of its own and remains in the media and apparently even with the architects of the “climate change vulnerability index”. The perpetrators of this falsehood are likely the real vulnerable parties having exposed themselves to lawsuits by countries suffering economic harm from their flawed prophecies of doom.

Cha-am Jamal

It is reported that there are 6.8 billion humans living on our planet but that it is endowed with natural resources and ecosystems that can support only 4.5 billion humans. The pressure on the ecosystem thus induced will cause a mass extinction of species by way of global warming and climate change. The scale of the mass extinction will be comparable with the extinction of dinosaurs  (UN urges action to save species, Bangkok Post, October 19, 2010). It is the old and completely discredited Paul Ehrlich Population Bomb hype of the 1960s and 1970s (2001 an Overpopulation Odyssey, Los Angeles Times, October 22, 1974). It has been resurrected to be recycled in the fancy new language of global warming and climate change apparently to present known falsehoods as climate science. The new global warming hype is thus exposed as nothing more than the old overpopulation pig with lipstick. It is a continuation of the movement by human beings against the habitation of the planet by other human beings but not themselves. This time around, not limited resource consumption, but carbon dioxide emission is presented as the proxy for destructive human activity. Ironically, in the same issue of the Bangkok Post, we read that Europeans are alarmed that phthalates in toys can damage the sexual development of children (The problem with hazardous phthalates, Bangkok Post, October 19, 2010). Those who really believe in the alleged dangers of overpopulation should be comforted by the population control effect of phthalates. That they are alarmed shows that the global warming mass extinction alarm is a lie disguised as science, and that overpopulation is not a concern that there are too many of us but that there are too many other people.

1960s: The over-population theory explores the fear that there are too many people on earth and they are breeding too fast. It is predicted that by 1987 human activity will exceed the planet’s ability to sustain us with food, energy, and raw materials. The scenario, explored in the movie “Soilent Green”, is predicted to includes Biblical famine and death, anarchy, and the devolution of human society possibly including cannibalism. Human activity will have destroyed the earth’s ability to sustain human beings.

1970s: The “limits to growth” theory disseminates the fear that society will collapse by the year 2000 because there is a hard upper limit to the amount of fossil fuels, minerals, and other planetary resources that we can consume and therefore a limit to the level of economic growth that is achievable. Continued economic growth will run into this upper limit and cause a complete collapse of civilization as we know it.

1970s: The first ozone depletion scare campaign is waged against the development of the SST high altitude airliner with the allegedly scientific argument that nitric oxide (NOx) in the jet exhaust will deplete ozone in the ozone layer. The campaign is successful and the SST program is canceled. Their success emboldens environmental extremists and the modern version of planetary environmentalism based on fear takes form. Twenty years later the same scientists, alarmed by falling NOx concentration in the lower atmosphere declared that “NOx is the immune system of the atmosphere” because it prevents chlorine from depleting ozone.

1980s: The second ozone depletion scare campaign is waged against refrigerants that contain CFC chemicals saying that human activity was causing an ozone hole over the Antarctic and causing the establishment of the Montreal Protocol and a comprehensive ban on the most efficient and inexpensive refrigerants used worldwide. The ozone depletion science is proven wrong but the media that helped hype the ozone hole scare are silent on the issue. The ozone hole scare quietly disappears from the media.

1990s to present: The global warming scare campaign rises like a Phoenix from the ashes of the failed ozone hole scare campaign with the theory that carbon dioxide from fossil fuels accumulates in the atmosphere, traps heat, and warms up the planet with catastrophic consequences of Biblical proportions.