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Carbon-dioxide (CO2) is the main contributor to anthropogenic global warming,and the timing of its peak concentration in the atmosphere is likely to governthe timing of maximum radiative forcing. It is well-known that dynamics ofatmospheric CO2 is governed by multiple time-constants, and here we approximatethe solutions to a linear model of atmospheric CO2 dynamics with fourtime-constants to identify factors governing the time-delay between peaks inCO2 emissions and concentrations, and therefore the timing of the concentrationpeak. The main factor affecting this time-delay is the ratio of the rate ofchange of emissions during its increasing and decreasing phases. If this ratiois large in magnitude then the time-delay between peak emissions andconcentrations is large. Therefore it is important to limit the magnitude ofthis ratio through mitigation, in order to achieve an early peak in CO2concentrations. This can be achieved with an early global emissions peak,combined with rapid decarbonization of economic activity, because the delaybetween peak emissions and concentrations is affected by the time-scale withwhich decarbonization occurs. Of course, for limiting the magnitude of peakconcentrations it is also important to limit the magnitude of emissionsthroughout its trajectory, but that aspect has been studied elsewhere and isnot examined here. The carbon cycle parameters affecting the timing of theconcentration peak are primarily the long multi-century time-constant ofatmospheric CO2, and the ratio of contributions to the impulse responsefunction of atmospheric CO2 from the infinite time-constant and the longtime-constant respectively. Reducing uncertainties in these parameters canreduce uncertainty in forecasts of the radiative forcing peak.

Factors controlling the time-delay between peak CO2 emissions and concentrations