A perspective on time: loss frequencies, time scales and lifetimes

Abstract

Environmental context The need to describe the Earth’s system or any of its components with a quantity that has units of time is ubiquitous. These quantities are used as metrics of the system to describe the response to a perturbation, the cumulative effect of an action or just the budget in terms of sources and sinks. Given a complex, non-linear system, there are many different ways to derive such quantities, and careful definitions are needed to avoid mistaken approximations while providing useful parameters describing the system. Abstract Diagnostic quantities involving time include loss frequency, decay times or time scales and lifetimes. For the Earth’s system or any of its components, all of these are calculated differently and have unique diagnostic properties. Local loss frequency is often assumed to be a simple, linear relationship between a species and its loss rate, but this fails in many important cases of atmospheric chemistry where reactions couple across species. Lifetimes, traditionally defined as total burden over loss rate, are mistaken for a time scale that describes the complete temporal behaviour of the system. Three examples here highlight: local loss frequencies with non-linear chemistry (tropospheric ozone); simple atmospheric chemistry with multiple reservoirs (methyl bromide) and fixed chemistry but evolving lifetimes (methyl chloroform). These are readily generalised to other biogeochemistry and Earth system models.