Quantifying memory and persistence in the atmosphere–land/ocean carbon system

Abstract. Here we interpret carbon dioxide (CO2) emissions from fossil fuel burning and land use as a global stress-strain experiment. We use the idea of a Maxwell body consisting of elastic and damping (viscous) elements to reflect the overall behaviour of the atmosphere–land/ocean system in response to the continued increase of CO2 emissions between 1850 and 2015. From the standpoint of a global observer, we see that as a consequence of the increase, the CO2 concentration in the atmosphere increases (rather quickly). Concomitantly, the atmosphere warms and expands, while part of the carbon is locked away (rather slowly) in land and oceans, likewise under the influence of global warming. It is not known how reversible and how much out of sync the latter process is in relation to the former. All we know is that the slower process remembers the influence of the faster one which runs ahead. Here we ask three (nontrivial) questions: (1) Can this global-scale memory–Earth’s memory–be quantified? (2) Is Earth’s memory a buffer which is negligently exploited; and in the case that it is even a limited buffer, what is the degree of exploitation? And (3) does Earth’s memory allow its persistence (path dependency) to be quantified? To the best of our knowledge, the answers to these questions are pending. We go beyond textbook knowledge by introducing three parameters that characterise the system: delay time, memory, and persistence. The three parameters depend, ceteris paribus, solely on the system’s characteristic viscoelastic behaviour and allow deeper insights into that system. We find that since 1850, the atmosphere–land/ocean system has been trapped progressively in terms of persistence (i.e., it will become progressively more difficult to strain-relax the system), while its ability to build up memory has been reduced. The ability of a system to build up memory effectively can be understood as its ability to respond still within its natural regime; or, if the build-up of memory is limited, as a measure for system failures globally in the future. Approximately 60 % of Earth’s memory had already been exploited by humankind prior to 1959. We expect system failures globally well before 2050 if the current trend in emissions is not reversed immediately and sustainably.