The exponential eigenmodes of the carbon-climate system, and their implications for ratios of responses to forcings CSIRO Marine and Atmospheric Research, Canberra, ACT 2601, Australia
25 Jan 2013
Received: 30 Jul 2012 – Published in Earth Syst. Dynam. Discuss.: 19 Sep 2012 Abstract. Several basic ratios of responses to forcings in the carbon-climate system
are observed to be relatively steady. Examples include the CO2 airborne
fraction (the fraction of the total anthropogenic CO2 emission flux that
accumulates in the atmosphere) and the ratio T/QE of warming
(T) to cumulative total CO2 emissions (QE). This paper
explores the reason for such near-constancy in the past, and its
likely limitations in future.
Revised: 30 Nov 2012 – Accepted: 22 Dec 2012 – Published: 25 Jan 2013
The contemporary carbon-climate system is often approximated as a set of
first-order linear systems, 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 the carbon-climate system is idealised as a linear system (Lin)
forced by exponentially growing CO2 emissions (Exp), then all
ratios of responses to forcings are constant. Important cases
are the CO2 airborne fraction (AF), the cumulative airborne fraction
(CAF), other CO2 partition fractions and cumulative partition fractions
into land and ocean stores, the CO2 sink uptake rate (kS,
the combined land and ocean CO2 sink flux per unit excess atmospheric
CO2), and the ratio T/QE. Further, the AF and the CAF are
equal. Since the Lin and Exp idealisations apply approximately to
the carbon-climate system over the past two centuries, the theory explains
the observed near-constancy of the AF, CAF and T/QE in this period.
A nonlinear carbon-climate model is used to explore how
future breakdown of both the Lin and Exp idealisations will cause the AF, CAF
and kS to depart significantly from constancy, in ways that depend
on CO2 emissions scenarios. However, T/QE remains
approximately constant in typical scenarios, because of compensating
interactions between CO2 emissions trajectories,
carbon-climate nonlinearities (in land–air and ocean–air carbon exchanges
and CO2 radiative forcing), and emissions trajectories for non-CO2 gases.
This theory establishes a basis for the widely assumed proportionality
between T and QE, and identifies the limits of
Citation: Raupach, M. R.: The exponential eigenmodes of the carbon-climate system, and their implications for ratios of responses to forcings, Earth Syst. Dynam., 4, 31-49, doi:10.5194/esd-4-31-2013, 2013.