# A MATHEMATICAL INCONSISTENCY

Posted on: August 26, 2020

THIS POST IS A COMPARISON OF THE ECS AND TCR, THE TWO METHODS USED INTERCHANGEABLY IN CLIMATE SCIENCE TO RELATE WARMING TO FOSSIL FUEL EMISSIONS. THE COMPARISON IS MADE IN TERMS OF MATHEMATICAL CONSISTENCY.

RELATED POST ON STATISTICS: LINK: https://tambonthongchai.com/2021/05/18/climate-science-vs-statistics/

THE EQUILIBRIUM CLIMATE SENSITIVITY ECS

The ECS measure of the impact of fossil fuel emissions on warming holds that atmospheric CO2 concentration at any given time is a linear function of cumulative emissions and that surface temperature is a logarithmic function of atmospheric CO2 concentration. These two relationships imply that surface temperature is a logarithmic function of cumulative emissions. That in turn implies that the amount of warming caused by a given level of cumulative emissions is the difference between the logarithms of the two cumulative emissions before and after.

TRANSIENT CLIMATE RESPONSE TO CUMULATIVE EMISSIONS TCR

The TCR measure of the impact of fossil fuel emissions on warming holds that the amount of warming is a linear function of cumulative emissions. This linearity is mathematically inconsistent with the ECS measure which implies that the amount of warming is proportional to the difference between the logarithms of the cumulative emissions before and after the period of warming under study.

IMPLICATIONS OF THIS MATHEMATICAL INCONSISTENCY

The mathematical inconsistency described above shows that the significant research effort in climate science to resolve the ECS and TCR measures of anthropogenic warming in terms of fossil fuel emissions with Earth System Models {ESM} is not possible because the two methods of computing the impact of emissions on temperature are not mathematically consistent and that makes it impossible for them to describe the same phenomenon in nature.

CONFIRMATION BIAS, CIRCULAR REASONING, AND MATHEMATICAL IMPOSSIBILITY OF EARTH SYSTEM MODELS {ESM}

In a related post on ESM {https://tambonthongchai.com/2020/08/25/earth-system-models-and-carbon-budgets/} we argue that the ESM construction procedure of beginning with the TCR warming derived from cumulative emissions and then explaining the result from an arbitrarily expanded list of ECS climate drivers is a form of circular reasoning. In this post we find that a further and more serious flaw in this procedure is the mathematical impossibility of the ESM exercise of reconciling ECS and TCR .

Yet another issue with the TCR and its Earth System Model application is that the TCR is based on a spurious correlation as shown in a related post:

RELATED POST: WHAT THE TCRE TELLS US ABOUT CLIMATE SCIENCE

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• Laurence Hunt: Oh yeah, I reposted on Twitter.
• Laurence Hunt: I take global warming as a serious issue, though I favour private (investment-based) solutions to anticapitalism, government expansion and tax increas