Diagnostic timescales in fluid flows: from partial differential equations to simple models

For geophysical and environmental flows, diagnostic timescales (e.g., age, residence/exposure time) may be obtained at any time and position by solving the partial differential equations established in the framework of CART (Constituent-oriented Age and Residence time Theory, www.climate.be/cart). Such timescales are holistic in that they take into account in the whole domain of interest (advective and diffusive) transport as well as reactive processes. They may be instrumental in the development of reduced-complexity models such as a well-mixed box and various types of pipe flows (or a combination of such idealizations), aiming at interpreting the results of complex models. Illustrations are provided, focusing on the global water age distribution in the World Ocean, the top layer of Lake Tanganyika and the Scheldt Estuary. Clearly, diagnostic timescales paint a picture of the functioning of numerical models of reactive transport that is different from that obtained by analyzing primitive variables.