A moisture function of soil heterotrophic respiration that incorporates microscale processes.

Soil heterotrophic respiration (HR) is an important source of soil-to-atmosphere CO flux, but its response to changes in soil water content (θ) is poorly understood. Earth system models commonly use empirical moisture functions to describe the HR-θ relationship, introducing significant uncertainty in predicting CO flux from soils. Generalized, mechanistic models that address this uncertainty are thus urgently needed.

Transit times and mean ages for nonautonomous and autonomous compartmental systems.

We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick-von Förster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary differential equation that is exponentially stable. We then define a nonautonomous version of transit time as the mean age of mass leaving the compartmental system at a particular time and show that our nonautonomous theory generalises the autonomous case.