Two main concepts help as diagnostics of ecosystem processes and ecosystem models of biogeochemical cycling, the age of the mass of an element in a system at a given time, and the age of the mass in the output flux at a given time. These concepts, namely system age and transit time, are very useful metrics to compare ecosystem processes along environmental gradients, compare model predictions among each other, and contrast observations against models. However, there is confusion on the application of these concepts to applied problems, and for many applications, there were not yet explicit formulas for their computation. In this contribution, we will a) propose rigorous definitions for system age and transit times of biogeochemical elements in ecosystems, and b) present new mathematical formulas for the computation of system age and transit time distributions for linear and non-linear systems as well as systems out of steady-state. In addition, we applied these formulas to estimate ages and transit times of carbon in some terrestrial ecosystems.
Results/Conclusions
We found that 1) mean system ages are always older than mean transit times for systems in equilibrium, but the reverse can be observed in some systems out of equilibrium such as in the case of soil carbon emission from permafrost thawing. 2) Ecosystem compartments are always a mix of carbon of multiple ages, the slower the cycling rate of the compartment, the larger the spread of ages. 3) Ages and transit time distributions can be approximated by the Phase-Type distribution for systems in equilibrium, for systems out of a steady-state the time-varying density distributions depend on the initial age distribution in the system, temporal changes in element inputs and cycling rates, and the structure of the 'state transition operator', a mathematical function that defines the trajectories of change in the state of ecosystems. We also show other applications of this framework such as the study of model structures for vegetation models, and the estimation of the time fossil fuel carbon would reside in the atmosphere under different emission scenarios.