Retrieving the age of air spectrum from tracers: principle and method

Surface-emitted tracers with different dependencies on transit time (e.g., due to chemical loss or time-dependent boundary conditions) carry independent pieces of information on the age of air spectrum (the distribution of transit times from the surface). This paper investigates how and to what extent knowledge of tracer concentrations can be used to retrieve the age spectrum. Since the mixing ratios of the tracers considered depend linearly on the transit time distribution, the question posed can be formulated as a linear inverse problem of small dimension. An inversion methodology is introduced, which does not assume a prescribed shape for the spectrum. The performance of the approach is first evaluated on a constructed set of artificial radioactive tracers derived from idealized spectra. Hereafter, the inversion method is applied to outputs of a chemistry–transport model. The latter experiment highlights the limits of inversions using only parent radioactive tracers: they are unable to retrieve fine-scale structures such as the annual cycle. Improvements can be achieved by including daughter decaying tracers and tracers with an annual cycle at the surface. This study demonstrates the feasibility of retrieving the age spectrum from tracers and has implications for transport diagnosis in models and observations.