# The Remaining Carbon Budget Anomaly Explained

Posted December 25, 2019

on:**Carbon budgets are derived from the TCRE (Transient Climate Response to Cumulative Emissions) correlation between cumulative warming and cumulative emissions. The value of the TCRE is the regression coefficient of cumulative warming against cumulative emissions.****In related posts it is shown that the TCRE correlation derives not from the responsiveness of warming to emissions but from a sign pattern in which annual emissions are always positive and, during a a warming trend, annual warming is***mostly*positive. [LINK] [LINK] [LINK] .**Since emissions are always positive, the***TCRE regression coefficient*in this proportionality is determined by the fraction of annual warming values that are positive. Larger fractions of positive warming values yield higher values of the TCRE regression coefficient and it is the regression coefficient that determines the value of the carbon budget.**Because of the random nature of the annual warming values, it is highly unlikely that the fraction of annual warming values that are positive in the full span of the carbon budget period will be the same as the fraction of annual warming values that are positive in the two halves of the full span.****Therefore we find that in general the TCRE regression coefficient for the full span of the carbon budget period, that for the first half of the carbon budget period, and that for the second half of the carbon budget period will be different.****It is this simple statistical issue that imposes the remaining carbon budget problem because for the carbon budgets in the two halves of the carbon budget period to be the same, the positive fraction of the annual warming values would have to be the same in the two halves and in general they are not and that creates the Remaining Carbon Budget anomaly.***Therefore, the Remaining Carbon Budget anomaly does not have an interpretation in terms of the climate science of additional forcings or feedbacks in climate models or of additional climate variables in earth system models – but an interpretation only in terms of the statistics of the fraction of annual warming values that are positive*.**The more relevant consideration is of course that the TCRE regression coefficient has no interpretation in terms of climate phenomena because it is a spurious statistic – a creation of the oddities of the time series of the cumulative values of another time series as described in related posts****[LINK]****[LINK]**.

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