Making sense of ZEC and TCRE: A conceptual model for the coupled climate response to carbon emissions.

Effective climate policy requires quantifying the temperature response to CO₂ emissions. The current policy framework centers around Remaining Carbon Budgets, and depends heavily on there being a linear Transient Climate Response to Cumulative Emissions (TCRE) and a low Zero Emission Commitment (ZEC). The linearity of TCRE and the smallness of ZEC are based on emergent behaviors of a small number of Earth System Models (ESMs) and lack both conceptual understanding and uncertainty quantification. 

Here we present an analytically tractable conceptual model for the coupled interaction of the thermal component of the climate system with the carbon cycles.  Unlike previous decompositions our model is built by assembling dynamical energy balance and carbon flux models. Thus, we obtain closed-form approximations for TCRE and ZEC in terms of well-established conceptual parameters such as the radiative feedback, ocean heat uptake efficiency, the average timescale ocean carbon uptake, the Q10 temperature sensitivity of respiration, etc. 

We derive conditions for both long-term (millennial-scale) low ZEC, as well as conditions for transient (centennial-scale) low ZEC, along with conditions for the near-linearity of TCRE. We find that there is no intrinsic physical reason for a low ZEC or a linear TCRE, and they arise from fortuitous compensations between unrelated parameters. We also show the system has the potential for significant centennial-scale transient amplification, arising from non-normal system dynamics.

In addition to providing conceptual insight, the model allows us to easily explore the limits of the traditional assumptions surrounding TCRE and ZEC. For example, we show that a pattern effect derived from models with observed Sea Surface Temperature patterns (AMIP), can lead to a much larger ZEC than that derived from coupled ESMs.