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

Abstract. Here we intend to further the understanding of the planetary burden (and its dynamics) caused by the effect of the continued increase in carbon dioxide (CO2) emissions from fossil fuel burning and land use as well as by global warming from a new rheological (stress–strain) perspective. That is, we perceive the emission of anthropogenic CO2 into the atmosphere as a stressor and survey the condition of Earth in stress–strain units (stress in units of Pa, strain in units of 1) – allowing access to and insight into previously unknown characteristics reflecting Earth's rheological status. We use the idea of a Maxwell body consisting of elastic and damping (viscous) elements to reflect the overall behavior of the atmosphere–land and ocean system in response to the continued increase in CO2 emissions between 1850 and 2015. Thus, from the standpoint of a global observer, we see that the CO2 concentration in the atmosphere is increasing (rather quickly). Concomitantly, the atmosphere is warming and expanding, while some of the carbon is being locked away (rather slowly) in land and oceans, likewise under the influence of global warming. It is not known how reversible and how out of sync the latter process (uptake of carbon by sinks) is in relation to the former (expansion of the atmosphere). All we know is that the slower process remembers the influence of the faster one, which runs ahead. Important questions arise as to whether this global-scale memory – Earth's memory – can be identified and quantified, how it behaves dynamically, and, last but not least, how it interlinks with persistence by which we understand Earth's path dependency. We go beyond textbook knowledge by introducing three parameters that characterize the system: delay time, memory, and persistence. The three parameters depend, ceteris paribus, solely on the system's characteristic viscoelastic behavior and allow deeper and novel insights into that system. The parameters come with their own limits which govern the behavior of the atmosphere–land and ocean carbon system, independently from any external target values (such as temperature targets justified by means of global change research). We find that since 1850, the atmosphere–land and ocean system has been trapped progressively in terms of persistence (i.e., it will become progressively more difficult to 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. Based on these stress–strain insights we expect that the atmosphere–land and ocean carbon system will be forced outside its natural regime well before 2050 if the current trend in emissions is not reversed immediately and sustainably.