Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Abstract Several basic ratios describing the carbon-climate system are observed to adopt relatively steady values. Examples include the CO 2 airborne fraction (the fraction of the total anthropogenic CO 2 emission flux that

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... in the atmosphere) and the ratio T/Q E of warming (T ) to cumulative total CO 2 emissions (Q E ). This paper explores 5 the reason for such near-constancy in the past, and its likely limitations in future. The contemporary carbon-climate system is often approximated as a first-order linear system, for example in response-function descriptions. All such linear systems have exponential eigenfunctions in time (an eigenfunction being one that, if applied to the system as a forcing, produces a response of the same shape). This implies that, if 10 the carbon-climate system is idealised as a linear system (Lin) forced by exponentially growing CO 2 emissions (Exp), then all ratios among fluxes and perturbation state variables are constant. Important cases are the CO 2 airborne fraction (AF), the cumulative airborne fraction (CAF), other CO 2 partition fractions and cumulative partition fractions into land and ocean stores, the CO 2 sink uptake rate (k S , the combined land and ocean 15 CO 2 sink flux per unit excess atmospheric CO 2 ), and the ratio T/Q E . Further, the AF and the CAF are equal. The Lin and Exp idealisations apply approximately (but not exactly) to the carbon-climate system in the period from the start of industrialisation (nominally 1750) to the present, consistent with the observed near-constancy of the AF, CAF and T/Q E in this period. 20 A nonlinear carbon-climate model is used to explore how the likely future breakdown of both the Lin and Exp idealisations will cause the AF, CAF and k S to depart significantly from constancy, in ways that depend on CO 2 emissions scenarios. However, T/Q E remains approximately constant in typical scenarios, because of compensating interactions between emissions trajectories, carbon-cycle dynamics and non-25 CO 2 gases. This theory assists in establishing both the basis and limits of the widelyassumed proportionality between T and Q E , at about 2 K per trillion tonnes of carbon. Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion 20 is forced with exponentially growing anthropogenic CO 2 emissions (Exp). In this idealisation, constant ratios include the CO 2 airborne fraction, its cumulative counterpart, other CO 2 partition fractions, the CO 2 sink uptake rate, and the ratio T/Q E . These predictions are tested directly against observations. Finally, in Sect. 4, the predictions of the LinExp idealisation are compared with predictions from a nonlinear model of the 25 carbon-climate system, to investigate the applicability of the LinExp idealisation to future projections. Mathematical and modelling details are given in Appendices A and B, respectively. Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion