Residence time is a measure of the average time a substance spends within a physical system; this substance could be any particle flowing with the water. In the case of the coastal ocean a measure of residence time can be extremely useful in determining transport and fate of contaminants and organisms in estuarine systems. High resolution hydrodynamic models can be used to calculate residence time in coastal estuaries in more thorough ways than by observations alone. Methodologies for computing residence time and related variables have been investigated and developed by MMAP for ecological applications of coastal hydrodynamic models.
Generation of Residence/Flushing Time Maps from Numerical Ocean Model Prediction Fields
Residence time and flushing time are indicators of how long a pollutant or a biological organism will reside in a bay/estuary before being forced out of its mouth due either to river discharge or tidal flow. Therefore, a spatial map of the residence/flushing time of an estuary can be very beneficial. Generally, residence times can be estimated from numerical models by using Lagrangian particle tracking and flushing times can be estimated by using tracer patches.
In this research project, Rutgers University’s Regional Ocean Modeling System (ROMS) is applied to a simple 2D model problem and the model output fields are used to estimate residence/flushing times using a variety of methods which are compared with each other. Thereafter, these time scales will be displayed in the form of spatial maps as a function of the computational domain. It is expected that the insights gained from this model problem will also be applicable to more complex configurations such as the full 3D baroclinic circulation in bays and estuaries involving tracer (typically temperature and salinity) transport.
A simple 2D model problem computational domain is shown in Figure 1. It has a circular incursion roughly representing a bay and the flow is forced from the left hand boundary and passes through the domain to the right. The velocity along the xaxis is prescribed as U(y)=Asin(Ωt)+By/L with A=0.06 m/s, B=0.05 m/s, L=10000 m and Ω=2π/12 hr1. Hence, the ensuing flow is of a tidal nature with a period of exactly 12 hours. The southern boundary is of a noslip type and the right hand boundary is an open boundary.
This model problem has a steadystate solution as shown via the volumeaveraged kinetic energy plot in Figure 2. Solutions such as these together with a tidal period of exactly 12hours (0.5 days) enable the computation of steady residual velocity fields.

Figure 2 Volumeaveraged specific kinetic energy time history showing steadystate behavior. 
There are three basic residence/flushing time calculation methods which are investigated. They are the: (i) Lagrangian particle method, (ii) tracer patch method and, (iii) residual current method. In (i), an ensemble of particles are introduced in to the “bay” at time = 5.0 days (see Figure 2), tracked in space and time, and are taken to have exited the bay upon crossing the x=7000 m vertical line (Figure 1). Only the first crossing of the line by each particle is counted and subsequent crossings (due to the tidal motion of the flow) are ignored. In (ii), multiple tracer patch ensembles are activated within the “bay” and advected in two dimensions using the ROMS generated velocity fields. Both forward Euler and Leapfrog numerical algorithms for advection were investigated. The Leapfrog algorithm showed superior performance but required the inclusion of both time and spatial filtering to remove numerical oscillations. Residence/flushing times were evaluated by monitoring the tracer concentration levels at the x=7000 m line (Figure 3) or by determining the time of either (a) the global peak concentration level or (b) a predefined concentration level. With (iii), residual currents in time are calculated from time=5.0 days onwards, thus avoiding the transient startup phase. For time integration, rectangle, trapezoidal and Simpson’s rules were examined, with Simpson’s rule giving the optimal outcome. Thereafter, using this residual current field, residence/flushing times are obtained via (a) Lagrangian particle path tracking [as in (i)] and (b) tracer patch advection [as in (ii)] where this velocity field is kept invariant in time. Figure 4 is a plot of the residual velocity magnitude with corresponding velocity vectors.


Figure 4. Residual current plot using Simpson's rule. 
The residence/flushing time maps corresponding to (i), (ii), (iiia), and (iiib) are given in Figures 58. It is seen that the residence/flushing time estimates from the four different approaches are comparable and consistent with each other, demonstrating that the estimation methods are reliable and robust.
In summary, tracer patches require expensive computations due to the solution of advection equations for each ensemble and the need for many such ensembles to generate residence/flushing time maps. This approach is most easily achieved as a postprocessing exercise outside an ocean model. Furthermore, residence/flushing time maps generated with tracers is limited in resolution to the horizontal resolution of the model computational grid and, to achieve accurate estimates, frequently saved velocity fields are required which generate files very large in size. Particles, on the other hand, are cheaper computationally, can be tracked within ocean models easily, can be counted more decisively (as they are discrete), and allow the resolution of the spatial residence/flushing time maps to be controlled via the spatial density of particles (and can be placed on a subgrid scale). To generate realistic residence/flushing time estimates, both approaches will need to incorporate some dispersion, the mathematical formulations of which may not be straightforward and require further investigation.
National Ocean Service Workshop on Residence/Flushing Times in Bays and Estuaries, June 89, 2004
Residence times are extremely useful in determining water contamination and nutrient levels, distributions of organisms, and their spatiotemporal variations in bays and estuaries. Therefore, it is important to know if hydrodynamic circulation models could provide higherresolution estimates of residence times in bays, estuaries and small embayments within them than those available from (simpler) box models and direct measurements. To facilitate this, a workshop entitled "NOS Workshop on Residence/Flushing Times in Bays and Estuaries", funded through a NOS Partnership Project, was held at NOAA in Silver Spring, MD, in June 2004. The objectives of the workshop were to investigate: (i) the scope of applications of residence times, (ii) the state of the art methods for the calculations of residence times, (iii) the measurements required to evaluate residence times and (iv) with respect to the use of numerical hydrodynamic models, (a) the various numerical techniques used to determine residence times and (b) comparisons of the Lagrangian (particle tracking) versus Eulerian (tracer patch) approaches to computing residence times.

Figure 9. Map showing residence times in Houston Galveston area. 
Thirtyfour experts from academic institutions, private industry and government organizations participated in the two day workshop, which consisted of a sequence of invited talks (from the pool of participants) followed by three concurrent breakout sessions on the topics of applications, measurements and algorithms associated with the determination of residence times. Present shortcomings and future directions were also discussed and summaries of these are included in this report.
The conclusions and recommendations resulting from this workshop are: (1) that there is a hierarchy of models that can be used to assess transport time scales and that often the lower resolution models are sufficient; (2) when higher resolution is required hydrodynamic models can be used to compute residence times via (2a) the concentration patch approach, (2b) the Lagrangian particle path approach, (2c) the residual velocity and salinity intrusion method and (2d) the dynamical systems approach (with the use of Synoptic Lagrangian Maps); it is desirable (3) to calibrate (2a) against (2b) with an appropriate form of numerical dispersion included in the latter; (4) to compare the various residence time estimates resulting from the above four approaches ((2a)(2d)); and (5) to examine residence times in several well known bays and estuaries for which observed data are available.
Resources and Related Information:
Report on the National Ocean Service Workshop on Residence/Flushing Times in Bays and Estuaries(Adobe PDF)
This website contains useful links associated with Residence/Flushing times and also a downloadable NOAA Technical Report which describes the workshop in full detail.
