A decrease in the age of respired carbon from the terrestrial biosphere and increase in the asymmetry of its distribution.

We provide here a model-based estimate of the transit time of carbon through the terrestrial biosphere, since the time of carbon uptake through photosynthesis until its release through respiration. We explored the consequences of increasing productivity versus increasing respiration rates on the transit time distribution and found that while higher respiration rates induced by higher temperature increase the transit time because older carbon is respired, increases in productivity cause a decline in transit times because more young carbon is available to supply increased metabolism. The combined effect of increases in temperature and productivity results in a decrease in transit times, with the productivity effect dominating over the respiration effect. By using an ensemble of simulation trajectories from the Carbon Data Model Framework (CARDAMOM), we obtained time-dependent transit time distributions incorporating the twentieth century global change. In these simulations, transit time declined over the twentieth century, suggesting an increased productivity effect that augmented the amount of respired young carbon, but also increasing the release of old carbon from high latitudes. The transit time distribution of carbon becomes more asymmetric over time, with more carbon transiting faster through tropical and temperate regions, and older carbon being respired from high latitude regions. This article is part of the Theo Murphy meeting issue 'Radiocarbon in the Anthropocene'.

Stochastic and deterministic interpretation of pool models.

Carbon and element cycling models can be expressed in terms of the dynamics of individual particles or collection of them in aggregated pools. In both cases, the models represent the same dynamics and provide similar predictions. The time required for individual particles to pass through a system, that is, the transit time, can be obtained from both approaches. Pool models can be analyzed from a stochastic or a deterministic point of view.

Transit-time and age distributions for nonlinear time-dependent compartmental systems.

Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

The muddle of ages, turnover, transit, and residence times in the carbon cycle.

Comparisons among ecosystem models or ecosystem dynamics along environmental gradients commonly rely on metrics that integrate different processes into a useful diagnostic. Terms such as age, turnover, residence, and transit times are often used for this purpose; however, these terms are variably defined in the literature and in many cases, calculations ignore assumptions implicit in their formulas. The aim of this opinion piece was i) to make evident these discrepancies and the incorrect use of formulas, ii) highlight recent results that simplify calculations and may help to avoid confusion, and iii) propose the adoption of simple and less ambiguous terms.