The Constituent-oriented Age and Residence time Theory : a holistic approach to the understanding of the results of complex geophysical and environmental fluid flow models
Nowadays geophysical and environmental fluid flow models routinely produce large amounts of results. Making sense of all these real numbers is not a trivial task. This is why specific interpretation methods are needed, such as, among others, estimating timescales. In this respect, a comprehensive theory (CART) is developed that allows for the estimation of timescales, mainly the age and the residence time, from the solution of partial differential problems.
At any time and position, the age — a measure of the elapsed time since a given origin — of every constituent, or group of constituents, of seawater can be estimated in such a way that advection, diffusion and production/destruction are properly taken into account. This method has been used to diagnose mass transfers in eco-system models of various degrees of complexity, help understand flow in estuaries, shallow seas and the World Ocean, and to develop reduced-dimension models, such as the leaky funnel, a metaphor of the ventilation of the World Ocean.
The residence time is usually defined as the time taken by a water/tracer parcel to leave the domain of interest. In the framework of CART, a rigorous generic method is suggested for evaluating, at any time and position, the residence time. An alternative version of the latter, the exposure time, is also considered so as to account for the fact that constituent particles can re-enter the domain of interest after leaving for the first time. This concept was applied in numerous situations, including a contribution to the study of a long-standing problem of marine biology, i.e. the question of how sinking phytoplankton species manage to survive.
Water renewal refers to the processes by which water initially in a semi-enclosed domain is progressively replaced by water originating from its environment. The rate at which water is renewed may be characterised by having recourse to the aforementioned timescales. This was exemplified by several publications focussing on the water renewal of the Scheldt Estuary (Belgium / The Netherlands). The relationship between water renewal, connectivity and the concept of exposure is also being explored, by means of theoretical developments, idealised models and realistic numerical simulations.
CART has been designed in such a way that it can be applied to reactive transport problems of any nature. Accordingly, new timescales can more of less easily be cast in the CART framework (see, e.g., an application to urban hydraulics).