The carbon budget concept (TCRE; Transient Climate Response to cumulative carbon Emissions) emerged as a major concept in climate research since the late 2000s. Due to its simplicity, it is intensively utilized in the international policy arena. It is based on the claim that one can derive the global mean temperature increase solely from the knowledge of historical cumulative emissions by observing the linear relationship between the two, regardless of the emission pathway that preceded ('pathway independence').
Here, we ask for the maximally possible deviations from the TCRE ideal across emission scenario space. While there has been an extensive focus on quantifying the carbon budget using highly complex climate models, there seems to be a lesser focus on the pathway independence and possibly related deviations from the budget. Furthermore, few analytical examinations have been presented, for highly stylized settings only. This study contributes to filling that gap, utilizing the energy balance model FAIR. FAIR incorporates climate feedbacks and correctly emulates the temperature response to an emission pulse.
If the carbon budget approach was perfectly valid, the temperature response to an emitted unit of carbon should be a perfect step function. The actual temperature evolution following the emission pulse is reinterpreted as a Green's function and as such, utilized to calculate the total temperature increase at any given point. The novelty in this work is that the emission pathway is not assumed, but generated by maximizing (minimizing) the temperature output.
With the boundary conditions being the fixed total cumulative emissions and the maximal allowed mitigation efforts, two associated pathways are generated with the temperature increase in a given year acting as an objective value. The deviation from the budget is then extracted as a temperature difference between the upper and the lower bound of the optimization process. The results show that the absolute value of the deviation is less than the standard deviation of climate variability, confirming the fundamentals of the carbon budget approach. We also present an analytical upper bound of the deviation from path independence. The result shows that the deviation is a function of the allowed maximum emission slope.
The advantage of this method is that it can utilize the impulse response properties already published for highly complex models. The current limitation of the presented approach lies in the assumption that the pulse response is assumed constant even though the climate changes. The implications of a changing pulse remain to be explored. We see our work as a twofold contribution: (i) to predict maximally possible TCRE deviations from already published impulse response experiments, and (ii), to generate analytic understanding for the driving variables.