Advanced Ocean Modelling: Using Open-Source Software

88 3 Basics of Nonhydrostatic ModellingResidence time is the time it takes for a virtual water parcel to escape from a givenarea. Particle-tracking methods, using Lagrangian floats such as in Exercise 9, areused to calculate this timescale. For the circulation shown in Fig. 3.51, for instance,the residence time of a water parcel released at point A is the time it takes until itreaches the exit boundary at point B. In this sense, a map of residence times can beconstructed for the entire region of interest. With consideration of parcels enteringthe region from outside, it is also possible to calculate a mean transit time includingstandard variation for a region of interest. Knowledge of residence times are usefulfor management of oil spills and identification of “shadow” regions of little flow.Flushing time is the time it takes for the water volume of a given region to be(almost) fully replaced by ambient water. Flushing times are computed using Euleriantracer fields such as in Exercise 9. To this end, tracer concentrations of unity areinitially allocated to the region of interest whereas concentrations are kept at zerovalue outside during the simulation. Flushing times can then be estimated as thetime is takes until concentration has dropped below a certain threshold value usuallytaken at exp (−π) ≈ 0.04. This implies that a region is considered flushed whenabout 96% of its initial water has been replenished with waters from a pre-definedsource region. The resultant flushing time distribution depends on the start time ofthe simulation. Distributions of flushing times are useful to illustrate regions thatare relatively stagnant. For the situation displayed in Fig. 3.51, for example, we cananticipate delayed flushing along the coastal zones and inside the centre of the eddyin Fig. 3.51.Age of a virtual water parcel or water volume is the time elapsed since ithas entered the system (Deleersnijder et al., 2001). When formulated by meansof Lagrangian floats, age tracking is similar to the calculation of residence time.When using a large number of floats, which can be computationally “expensive”,the Lagrangian method reveals age distributions within a grid cell as a function ofboth location and time. Nevertheless, water age is usually calculated from Eulerianconcentration fields according to the modified advection-diffusion equation:∂ A+ Adv(A) = Diff(A) + 1 (3.82)∂tFig. 3.51 Schematic forexplanation of residence timeand flushing time. Shadedareas represent regions ofdelayed flushing