# Partial ages: diagnosing transport processes by means of multiple clocks

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## Abstract

The concept of age is widely used to quantify the transport rate of tracers - or pollutants - in the environment. The age focuses only on the time taken to reach a given location and disregards other aspects of the path followed by the tracer parcel. To keep track of the subregions visited by the tracer parcel along this path, partial ages are defined as the time spent in the different subregions. Partial ages can be computed in an Eulerian framework in much the same way as the usual age by extending the Constituent oriented Age and Residence Time theory (CART, www.climate.be/CART). In addition to the derivation of theoretical results and properties of partial ages, applications to a 1D model with lateral/transient storage, to the 1D advection-diffusion equation and to the diagnosis of the ventilation of the deep ocean are provided. They demonstrate the versatility of the concept of partial age and the potential new insights that can be gained with it.

## Keywords

Age Advection-diffusion Tracer methods## Notes

### Acknowledgments

Éric Deleersnijder and Éric J.M. Delhez are both honorary research associates with the Belgian Fund for Scientific Research (F.R.S.-FNRS).

This work was supported by the Fondation BNP Paribas through the project FATES (FAst Climate Changes, New Tools To Understand And Simulate The Evolution of The Earth System) in the scope of its *Climate Initiative* programme.

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