NOAA Technical Report NOS CS 20 

REPORT ON THE NOS WORKSHOP ON 

RESIDENCE/ FLUSHING TIMES IN BAYS AND 

ESTUARIES 

Silver Spring, Maryland 

September 2005 

n 0 a a National Oceanic and Atmospheric Administration 

U.S. DEPARTMENT OF COMMERCE 

National Ocean Service 

Office of Coast Survey 

Coast Survey Development Laboratory 
Office of Coast Survey 

National Ocean Service 

National Oceanic and Atmospheric Administration 

U.S. Department of Commerce 

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NOAA Technical Report NOS CS 20 

REPORT ON THE NOS WORKSHOP ON RESIDENCE/ 

FLUSHING TIMES IN BAYS AND ESTUARIES 

Frank Aikman, Ill 

Lyon W.J. Lanerolle 

September 2005 

n 0 a a National Oceanic and Atmospheric Administration 

U.S. DEPARTMENT 

OF COMMERCE 

Carlos Gutierrez, Secretary 

Office of Coast Survey 

National Oceanic and 

Atmospheric Administration 

Conrad C. Lautenbacher, Jr., 

VADM USN {Ret.), Under Secretary 

Captain Roger L. Parsons, NOAA 

National Ocean Service 

Richard W. Spinrad, Ph.D. 

Assistant Administrator 

Coast Survey Development 

Laboratory 

Mary Erickson 
NOTICE 

Mention of a commercial company or product does not constitute an 

endorsement by NOAA. Use for publicity or advertising purposes of 

information from this publication concerning proprietary products or the 

tests of such products is not authorized. 
Report on the National Ocean Service Workshop on 

Residence/Flushing Times in Bays and Estuaries 

Frank Aikman III 

 Office of Coast Survey, NOAA 

Lyon W. J. Lanerolle 

 Office of Coast Survey, NOAA 
Table of Contents

Executive Summary........................................................................................................... iv 

1. Introduction.................................................................................................................... 1 

2. Motivation: Some Background on Residence Time ...................................................... 2 

3. Workshop Objectives and Organization ........................................................................ 3 

4. Workshop Results and Outcomes.................................................................................. 4 

4a. Applications Session Summary................................................................................ 5 

4b. Measurements Session Summary ............................................................................ 6 

4c. Algorithms Session Summary.................................................................................. 6 

5. Summary, Recommendations and Future Directions ................................................. 7 

Acknowledgements........................................................................................................... 10 

References......................................................................................................................... 11 

Appendix A : Workshop Agenda...................................................................................... 13 

Appendix B : Summaries of the Presentations ................................................................ 15 

Appendix C : Attendees.................................................................................................... 20 

 iii
Executive Summary 

Residence times are extremely useful in determining water contamination and nutrient 

levels, distributions of organisms, and their spatio-temporal variations in bays and 

estuaries. Therefore, it is important to know if hydrodynamic circulation models could 

provide higher-resolution estimates of residence times in bays, estuaries and small 

embayments within them than those available from (simpler) box models and direct 

measurements. In order 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. 

Thirty-four 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 break-out 

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.

 iv
1. Introduction 

In 2003, the National Ocean Service’s (NOS) National Centers for Coastal Ocean 

Science (NCCOS) enquired if the hydrodynamic circulation models used by NOS’ Coast 

Survey Development Laboratory (CSDL) could provide spatially and temporally detailed 

estimates of residence times in bays, estuaries, and small embayments within them. This 

discussion grew into a proposal to the 2003 NOS Partnership Program, entitled Flushing 

and Residence Time Estimation Using NOS Estuarine Hydrodynamic Model-based 

Forecast Systems. We hypothesized that the sophisticated 3-dimensional hydrodynamic 

models that have been developed for many estuaries such as the Galveston Bay 

Operational Forecast System (GBOFS: see Schmalz, 2004) and the Port of New 

York/New Jersey Operational Forecast System (NYOFS: see Wei, 2003) would produce 

more refined estimates of residence time than those based on the traditional models and 

help better understand the factors that affect it. 

Residence time is an important factor in determining levels of contamination and 

concentrations of nutrients in a water body and their potential effects on estuarine 

organisms. It is commonly used in producing comparative assessments of how estuaries 

respond to human use. The calculation of residence time has been predominantly based 

on empirical studies using tracers (for example, salinity or dye), very simple box models 

or simple tidal prism models, and 1- and 2-dimensional models (see for example: Sheldon 

and Alber, 2002; Miller and McPherson, 1991; Hagy et al., 2000; and Signell and 

Butman, 1992) which have attempted to address some of the weaknesses associated with 

the simpler box models. We proposed to begin using the 3-dimensional hydrodynamic 

models that numerically represent the physics that dominate circulation in any particular 

estuary. Some of the advantages of using hydrodynamic models are: (i) no particular 

model/behavior for residence times is assumed and a more fundamental approach for 

calculating them is adopted (for example, using Lagrangian particles – Sections 2, 4c), 

(ii) due to high spatio-temporal resolution of model outputs, the spatio-temporal behavior 

of residence times (which is a local quantity – Section 2) can be investigated in domains 

of arbitrary size, and (iii) several numerical methods can be used with model outputs to 

calculate and compare residence times (for example, passive tracer dispersion analysis, 

Lagrangian particle path analysis, residual velocity and salinity intrusion analysis and 

Synoptic Lagrangian Map analysis – Section 5). 

The NOS Partnership proposal was funded and is being used (a) to support a visiting 

scientist with experience in residence time modeling to work with the NOS scientists, (b)

to sponsor a workshop with invited experts to discuss residence time estimation from 

numerical hydrodynamic models, and (c) to conduct an in situ passive tracer experiment 

in the Houston Ship Channel with which to evaluate the hydrodynamic model of the 

GBOFS system and to complete a similar effort previously carried out in New York 

Harbor (to evaluate the hydrodynamic model of the NYOFS system; seeWei et al., 2004). 

This report presents the results of the workshop, (b) above, held on June 8-9, 2004 in 

Silver Spring, MD. 

 1
2. Motivation: Some Background on Residence Time 

Estuarine ecosystems involve the transport of materials (e.g., nutrients, plants, animals, 

and suspended particles) in a fluid medium, and the transport phenomena involve a 

variety of time and space scales. Without breaking transport down to its constitutive 

processes (advection, diffusion, etc.), simple aspects of it can be determined by looking at 

some transport time scales which may overlook or amalgamate the underlying physical 

processes to a great extent. The transport time scales of interest to this workshop are age, 

residence and flushing time scales and, in particular, the residence time scale. Age is 

defined as the time a particle/fluid parcel has expended in order to travel to a specific 

location within a pre-defined region/control volume since entering it through one of its 

boundaries; therefore, it is unique to each particle/fluid parcel and particles/fluid parcels 

at different locations within this region have different ages. Residence time is how long a 

particle/fluid parcel starting at a specific location within this region, will take to leave it 

through one of its boundaries or alternatively, how long it will remain within this region 

before exiting it from one of its boundaries. The concepts of age and residence time are 

complementary to each other so that relative to a common spatial location within a 

region, age plus residence time equals transit time which is the total time that a 

particle/fluid parcel spends (between entrance and exit) in this region (Zimmerman, 

1976). Flushing time is defined as the time required to reduce the concentration of a 

tracer by a pre-determined factor (say an e-folding factor) within a given region. 

Flushing time is usually associated with tracers/dissolved materials (continuous 

quantities) and residence time and age are associated with both tracers/dissolved 

materials and particles (discrete quantities). Flushing time is an integrative quantity 

(thereby ignoring local processes and information) but residence time and age are 

(spatially) local quantities and are very useful in understanding locally occurring 

phenomena (Monsen et al., 2002; Sheldon and Alber, 2002). In this respect, the 

estimation and study of these times in localized regions such as bays and estuaries are 

particularly relevant. A more in depth discussion of the above mentioned transport time 

scales can be found in Zimmerman, 1976 and in Tekeoka, 1984. 

Residence times are extremely useful in determining, for example, pollutant 

concentrations, distributions of plankton (Basu and Pick, 1996), harmful algal blooms 

(Bricelj and Lonsdale, 1997), pelagic bacteria (Painchaud et al., 1996) and dissolved 

nutrients (Andrews and Muller, 1983) in bays and estuaries, all of which have a 

significant impact on humans. Some scientific investigators (Boynton et al., 1995) have 

argued that residence time is a sufficiently significant concept that it could form a basis 

for the comparative analyses of nutrient budgets in ecosystems (some examples on 

denitrification are given in Dettmann, 2001 and in Seitzinger, 2000)). Furthermore, due 

to the spatially local nature of residence times, they are very useful in identifying and 

quantifying spatially inhomogeneous phenomena and processes in sub-domains of bays, 

estuaries and ecosystems. 

Definitions and calculations of residence times, flushing times and ages do not always 

use consistent methods, and in most cases the models used for obtaining them (e.g. 

simple box models) are derived by assuming certain idealized flow conditions (e.g. 

complete and instantaneous mixing in the region of interest). There are, however, 

 2
important physical processes to take into account, such as tides which cause dissolved 

materials/tracers and particles/fluid parcels to oscillate in and out of bays, estuaries and 

any sub-domains of interest within them. Simple models, for example the low-order box 

models, are adequate if the concern is for the average condition in an entire bay or 

estuary, but they greatly underestimate, or do not address, the residence times associated 

with smaller regions with restricted circulation, such as urban harbors and embayments. 

Hence, exploring the different methods of estimating residence times is of paramount 

importance and was a key theme in this workshop. 

Traditionally, residence times have been evaluated using only measured data but in the 

past couple of decades, with the advent of sophisticated 3-dimensional numerical ocean 

models, much spatially and temporally extensive flow-field information (for example, 

water density, temperature, salinity and velocity distributions) can be produced from 

numerical simulations. These results, with their high spatial and temporal resolutions, 

can be used to achieve more refined estimates of residence time for the computational 

regions of application and also to determine the physical factors most affecting their 

values and spatial distributions. Residence times can be calculated either by an Eulerian 

approach (tracer/concentration) or by Lagrangian particle path/trajectory information. 

The former is ideally suited to simulate substance distributions in an entire bay or estuary 

and the latter for the simulation of the transport of a substance locally in various subdomains within a bay or estuary. The particle tracking approach is particularly useful in 

that particles carry localized flow-field information (salinity, temperature, velocities, etc.) 

while also being subject to the effects of the physical processes (for example, advection, 

diffusion, etc.). Because particles are discrete, it is easy to determine and examine their 

statistics (for example, counting them, testing whether they crossed a pre-defined 

boundary, etc.). In this workshop it was desired to explore these concepts to a greater 

extent and also discuss other techniques for estimating residence times from 

hydrodynamic model outputs. 

3. Workshop Objectives and Organization 

The objectives of the workshop were to discuss and assess: (1) applications of 

residence/flushing time computations (addressing such concerns as hazardous materials, 

port development, fish stock assessment, eutrophication, pollution); (2) the state of the art 

methods for the determination of residence time; (3) measurements required to derive 

residence time estimates and experimental observations required for numerical 

simulations; and (4), with respect to models, (4a) the various numerical models and 

techniques employed to quantify and evaluate residence and flushing times and (4b) 

comparisons of Lagrangian versus Eulerian and internal versus external (post-processed) 

numerical particle tracking methods. 

Approximately 60 people from academic, private industry and government organizations 

were identified and invited, based on their expertise, backgrounds and interests in the 

residence time topic. The actual workshop attendance was 34 people (see Attendees list, 

Appendix C). The workshop was structured around the three primary themes of 

Applications, Measurements and Algorithms (see Agenda, Appendix A) with speakers 

 3
invited to give brief talks in each of these theme areas (see Summaries of the 

Presentations, Appendix B). Following the first day of talks and follow-up discussions, 

breakout sessions were organized on each of the three theme areas with each session 

tasked with examining the theme, identifying shortcomings and recommending future 

focus to improve residence time estimation. The meeting concluded with the respective 

rapporteurs summarizing the outcomes of each of the respective sessions. 

4. Workshop Results and Outcomes 

The workshop opened with an introductory session (see Agenda, Appendix A) focused 

on the state of the art in residence time estimation, from the perspective of modeled 

transport and the concept of age (Cerco and Kim); to the variance in the definition of 

residence time found over a spectrum of estuaries (Jay); to the example of the Columbia 

River integrated observation and modeling system and its usefulness in characterizing 

residence time and other residual water properties (Baptista); and the challenge presented 

for Zinc in San Diego Bay (O’Connor). There were also discussions about whether 

calculations of residence times using Eulerian and Lagrangian methods are comparable. 

Often this may not be the case, because the processes to which these two approaches are 

applied are often different: Eulerian calculations for dissolved constituents usually treat 

the water-land boundary (including the bottom) as reflective, while for particulate 

materials this boundary is often treated as “sticky” or adsorptive (i.e. a sink). This session 

was followed by the three theme sessions focusing on applications, measurements and 

algorithms. 

The applications presentations included an example of a completed observational and 

modeling effort at understanding the fate of copper in San Diego Bay (Chadwick); a 

summary of the challenges and needs for refined residence time estimates with respect to 

waste site response and remediation (Klein and White); and a succinct summary of the 

limits and challenges associated with particle tracking and dye release in calibrated 

models (Blumberg). 

The session on measurements included a description of in situ tracer studies using the 

sulfur hexafluoride (SF6) tracer (Ho); a summary of dispersion estimates based on dye 

releases (Chant); and, as a lead in to the session on algorithms, a description of the impact 

of flooding and drying processes on numerical model-based estimates of residence time 

(Chen). 

The algorithms session included a description of SqueezeBox, a flow-scaled 1-

dimensional box model (Sheldon); the analysis of transport from synoptic Lagrangian 

maps (Wiggins); and the idea of generalized Lagrangian mean circulation (Hamrick). 

A summary of results of the three themed breakout sessions follows. 

 4
4a. Applications Session Summary 

For clarity, it became important to specify that this workshop is centered on flowinduced, hydraulic residence time. The group identified situations where knowledge of 

hydraulic residence time contributes to determining how long a chemical or particle 

would remain within a specified area. In almost no case was hydraulic residence time by 

itself considered sufficient information. Characteristics of the chemical or of the particle 

and its interaction with other substances can cause its residence time to be very different 

from that of a parcel of water. Nonetheless, estimating hydraulic residence time is an 

important part of an overall assessment of the fate and effects of man-made and natural 

inputs to any given space. 

Applications of residence time include determining the fate of hazardous waste spills, 

rates of accumulation of chemical contamination from chronic point and non-point 

sources in sediment, steady-state aqueous concentrations of nutrients, calculations of total 

maximum daily loads of municipal waste, and rates of export of fish eggs and larvae 

released within a bay. 

All estimates of residence times for such applications have been based, in effect, on box 

models with the precision of the estimate increasing as boxes become smaller and time 

scales shorter. The simplest estimates are sometimes all that is needed. For example, the 

relative susceptibilities of different estuaries to nutrient additions can be based on 

assuming whole estuaries to be single homogeneous boxes of a known volume. 

Residence time can then be defined by the annual average rate of freshwater addition. 

When the concern centers on chemical contamination, the need is for residence time 

within small boxes rather than entire estuaries. When the fate of spills or the movement 

of fish eggs is at issue not only are small spatial scales important but also the time scale 

of interest is much less than a year. These finer scale estimates of residence time are 

included in the fine mesh numerical models. The grid cells associated with such models 

are small in the horizontal (of the order of tens of meters), may include vertical 

stratification, and the times can be nowcasts, based on real-time water level and wind 

data. Fine mesh hydrodynamic models are available for about twenty of the major 

estuaries in the United States. So long as an experienced practitioner is available to do so, 

the models readily provide precise estimates of rates of transport between cells (the 

inverse of residence time within cells). This dependence on experienced modelers is 

exacerbated by the fact that the existing models are from a variety of Federal and state 

agencies and academic groups, and each group uses different modeling techniques and 

computer codes. At the general level, a modeler can understand all the hydrodynamic 

models, but actually using any particular model requires experience with that model. 

In the absence of an existing hydrodynamic model or of a modeler to use it and with a 

need for more spatial resolution than assuming estuarine-wide homogeneity, residence 

times can be estimated on the basis of the volume of the sub-estuarine areas and tidal 

prisms, fresh water inflow (if any), and salinity distributions (if not homogeneous). 

 5
4b. Measurements Session Summary 

Measurements (of, for example, salinity, currents, water levels) can be used for 

determining residence time and dispersion associated with estuaries provided that they 

include long-term data (for example, seasonal or at least a neap-spring tidal cycle). 

Measurements over only short times will lead to estimates that will miss important peaks 

in estuarine flushing cycles. In general, the minimum requirement for measurements is a 

longitudinal and cross-sectional salinity data set, which enables determination of the 

dispersion rate of an estuary; the diffusion coefficients can be determined from a tracer 

experiment. Even with the use of long-term data, the calculation of residence and 

flushing times is not straightforward. Extreme events such as storms resulting in strong 

winds and large river discharges may be the primary drivers of water transport in some 

areas but they can be entirely missed in even a long-term measurement program. 

The major difficulties in conducting field measurements are the resources of 

instrumentation and skilled manpower to maintain it. Furthermore, for extreme events the 

use of autonomous instruments (e.g. autonomous underwater vehicles (AUV)) is more or 

less a necessity. 

Before one can use numerical ocean models for the calculation of residence times, it is 

necessary to evaluate the models against measurements for any particular model 

application. With respect to model evaluation, it is necessary to define what is needed 

from the model (that is, the time and space scales of interest and resolution required) and 

to gain an understanding of the estuarine system before deciding what measurements are 

needed. The requirements are highly dependent on the location and the time scales 

associated with the modeling purpose. For many ecosystem management purposes, a set 

of 1-dimensional or 2-dimensional salinity and volumetric measurements over a multiyear time scale with a box model are sufficient to estimate residence time. 

For both residence and flushing time computations and model validation, a suitable 

subset of required instrumentation would include: low cost salinity sensors, bio- and geochemical sensors for nutrients, high frequency radar for surface currents, AUVs, and 

acoustic Doppler current profilers for velocity and sediment transport measurements.

4c. Algorithms Session Summary 

Residence times can be quantified in terms of volume fluxes or particle fluxes (Burwell et 

al., 2000). Those from particle tracking are rare and there were questions concerning 

availability of such data in the literature. In terms of observations, there are dissolved 

tracer concentration data but much less in the way of particle/drifter data. 

Lagrangian particle tracking is attractive because the particles have information 

associated with them (velocities, positions, temperature, etc.). However, a particle field 

and a tracer/concentration field would evolve differently in time because the latter 

inherently averages over a lower level of spatial dispersion. Realistic particle tracking 

 6
simulations should include some measure of dispersion (which is not trivial to determine, 

see Blumberg et al., 2004)) because experiments show that two floats/drifters placed at 

the same initial spatial location will follow different trajectories due to these dispersive 

effects. The tracking of particles can be performed either inside a numerical algorithm 

(internally) or externally as a post-processing exercise; some numerical studies have 

shown that the use of hourly numerical solutions enables the post-processing approach to 

yield results indistinguishable from those of the internal approach. It was also decided 

that for the post-processing approach, it is hourly instantaneous particle data that should 

be used and not hourly-averaged data. There was also an interest expressed in the backtracking (back in time) of particles and related algorithms (but they were not discussed) 

and the post-processing approach is ideally suited for this exercise. 

It was decided that the comparison of a simple laboratory model with predictions from 

various numerical ocean models was not worthwhile because it is already known that 

models can reproduce simplified and idealized laboratory setups relatively accurately. 

Residence time calculations for the realistic and more complex applications are 

numerically challenging and are of greater interest. For such applications, the spatial 

domains of interest (for example, size of a bay, estuary or segment there of) are of critical 

importance and the residence times are expected to vary widely depending on the choices 

made. In cases where only average residence times over large spaces are needed, a box 

model calculation is sufficient and sophisticated numerical ocean models are not needed. 

It was proposed that perhaps the most reasonable ways to achieve residence time 

estimates through the use of numerical ocean circulation models are via: 

1. The analysis of residual velocity and salinity intrusion fields over long durations, and 

2. The dynamical systems approach (Wiggins et al., 2005) where convergent/divergent 

zones are visible on the Synoptic Lagrangian Maps, although this approach requires 

the (pre) determination of some parameter values. 

Both these approaches require large numerical data sets (for example, three-dimensional 

velocity and tracer output fields from an ocean model also spanning a wide interval in 

time) containing much fine-resolution (in space and time) information. In this respect, 

these approaches may be regarded as being numerically the most rigorous and precise 

ways to estimate residence times. 

5. Summary, Recommendations and Future Directions 

Residence times can be estimated using the following approaches: 

(a) direct measurements (as in section 4b); 

(b) box models (and their relatively more sophisticated extensions – see 

Introduction); 

(c) hydrodynamic models (using concentration patches and/or particles); 

 7
(d) residual velocity and salinity intrusion methods (using observed data and/or 

hydrodynamic model outputs); and 

(e) the dynamical systems approach (via Synoptic Lagrangian Maps using 

hydrodynamic model outputs). 

If the concern is for the average condition in an entire bay or estuary, then simplified 

models (for example, (a) and (b) above) are adequate but they will greatly underestimate 

or fail to address the residence times associated with smaller regions, such as urban 

harbors and embayments, which can exhibit restricted circulation. The more 

sophisticated numerical ocean models can be the basis of improved estimates of residence 

time in these small sub-embayments. With respect to (a), (b) and (d) above, crosssectional salinity and long-term data on fresh water input are desirable, although this is 

not always feasible and in such cases numerical model output may be used as a proxy. 

Numerical models themselves can have problems during extreme events (e.g. during 

strong storm wind and river discharge events) and in such situations (a) and (b) are the 

most realistic options. 

Residence time research and analysis now involves the application of physically more 

sophisticated 3-dimensional circulation models (Burwell et al., 2000; Shen and Haas, 

2004) to sub-domains of bays and estuaries of arbitrary size (resulting in 3-dimensional 

gridded flow-field data over multiple time levels), and high resolution estimates of 

residence times can be achieved via (i) the concentration patch approach, (ii) the particle 

tracking approach (done internally or externally of an ocean model), (iii) the residual 

velocity and salinity intrusion approach and (iv) the Synoptic Lagrangian Map approach. 

The particle tracking approach requires the inclusion of some level of artificial dispersion 

in keeping with the levels of horizontal diffusion present in the ocean; hence, it may be 

necessary to examine several different dispersion-diffusion (Brownian motion related) 

formulations before selecting the most appropriate choice. The particle-related 

dispersion should be such that the particle paths are consistent with the dynamics of a 

passive tracer patch (Blumberg et al., 2004) and therefore, some cross-calibration tests 

between (i) and (ii) above may also need to be performed (as in Burwell et al., 2000) in 

order to verify this relationship. Using the above approaches, it is possible to construct 

maps of the variations of residence times in time and space over whole bays and 

estuaries; inhomogeneities in the distributions of these residence times will provide vital 

evidence in support of important locally occurring phenomena. 

It would be a worthwhile exercise to compare, contrast and document the estimates of 

residence times resulting from the above described different approaches for some well 

known bays and estuaries. Provided that there exist complete and quality controlled data 

sets for these bays and estuaries, residence time estimates can be calculated (1) directly 

from them (using for example, the simpler box models) and (2) from hydrodynamic 

model outputs where the models have been driven using this data. Such data sets will 

also serve to enable the determination of the artificial dispersion coefficients required in 

the tracking of Lagrangian particles. Special studies of interest could be (a) tidal 

(multiple entrant) and non-tidal situations and (b) situations involving variable surface 

forcings – from calm weather conditions to extreme conditions such as hurricanes. Due 

to the diverse and extensive nature of such a major exercise, it could perhaps form the 

 8
basis for a multi-institutional collaborative effort with each institution specializing in a 

particular facet of the project. 

 9
Acknowledgements 

The authors would like to thank all the participants in the workshop for a stimulating and 

provocative discussion on the topic of transport time scales in bays and estuaries. We are 

especially grateful to the speakers and, in particular, we would like to thank Joan Sheldon 

and Ed Dettmann for their significant critique and input to this report. 

 10
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Signell, R.P and B. Butman. 1992. Modeling tidal exchange and dispersion in Boston 

Harbor. J. Geophys. Res., 97, 15191-15606. 

Takeoka H. 1984. Fundmental concepts of exchange and transport time scales in a coastal 

sea, Continental Shelf Research, 3, 311-326. 

Wei, E. 2003. The new Port of New York and New Jersey Operational Forecast System. 

Bulletin of the American Meteorological Society, 84 (9), 1184-1186. 

Wei, E., T. Caplow and P. Schlosser. 2004. Solute dispersion modeling in New York 

Harbor. NOAA Technical Report NOS CS 18, 45p. 

Wiggins, S. R. and D. Small. Synoptic Lagrangian Maps and Lagrangian particle 

tracking, J. Dynamical Systems, 100(5), 1000-1010. 

Zimmerman, J. T. F. 1976. Mixing and flushing of tidal embayments in the western 

Dutch Wadden Sea. Part I: Distribution of salinity and calculation of mixing time scales. 

Neth. J. Sea Res. 10: 149-191. 

 12
Appendix A : Workshop Agenda 

NOS Workshop on Residence/Flushing Times in Bays and Estuaries

June 8-9, 2004 

1315 East-West Highway, SSMC3, 4th Floor Conference Room 

NOAA, Silver Spring, MD 20910 

Tuesday, June 8 

Overview (9-10:30am) 

Frank Aikman - Introductions and charge to workshop 

Current State of the Art 

Carl Cerco and Sung-Chan Kim – RT estimates from modeled transport and the 

concept of “age” 

David Jay – Some thoughts on the concept of residence time 

Antonio Baptista – The CORIE integrated observation and modeling system and 

its contribution to characterizing residual properties and RT 

Tom O’Connor – Modeling zinc in San Diego Bay 

Applications (11-12:30pm) 

Bart Chadwick – Modeling the fate of copper in San Diego Bay 

Lawrence Klein and Jessica White – Waste site response and remediation 

Alan Blumberg – Determining estuarine residence/flushing times 

Measurements (1:30-3:00pm) 

David Ho - SF6 tracer release experiments 

Bob Chant – Lagrangian observations of mixing in a stratified estuary 

Changsheng Chen – The impact of the flooding/drying process on the residual 

time in estuaries 

Algorithms (3:30-5:00pm) 

Joan Sheldon – SqueezeBox: Flow-scaled 1-D box models for estuary residence 

time estimates 

Steve Wiggins – Transport analysis using Synoptic Lagrangian Maps (SLMs): the 

dynamical systems approach 

John Hamrick – Generalized Lagrangian Mean (GLM) theory revisited 

Wednesday, June 9 

Breakouts (8:00-10:00am) 

Three teams, charged with examining each theme and making recommendations 

back to workshop (using: examples; problems; possible solutions) 

Rapporteurs: 

Applications – Tom O’Connor 

 13
Measurements – Eugene Wei 

Algorithms – Lyon Lanerolle 

Breakout Team Reports/Discussion (10:30-12:00pm) 

Adjourn (12:30pm) 

 14
Appendix B : Summaries of the Presentations 

Introduction and charge to the workshop (Frank Aikman III) 

Beginning with a definition of Residence Time (RT), the following two questions were 

posed: (i) is residence time more appropriate to describe times associated with particles 

or particle ensembles? and (ii) is flushing time best suited for times associated with tracer 

concentrations? Thereafter, the objectives of the workshop were stated as the 

dissemination of the current state of the art in residence times (techniques, methods, etc.), 

applications of residence times, measurements/observations and their use in estimating 

residence times and algorithms for calculating residence times (both Eulerian and 

Lagrangian approaches). Finally, the desired outcomes were stated as numerical model 

intercomparisons, “who needs what?” (for example, chemists, biologists, etc.), a 

workshop report (with potential reviewers and editors) and “what is next?” (current 

shortcomings and future recommendations). 

RT estimates from modeled transport and the concept of “age” (Carl Cerco & 

Sung-Chan Kim) 

Several definitions for residence and flushing times were provided via the first moment 

of concentration, salinity concentration variation (with observed data), age (using a 

partial differential equation), dye releases and particle path tracking approaches. These 

various estimates were then compared and contrasted for Chesapeake Bay. In 

conclusion, it was said that (i) no single time scale describes all of the transport processes 

and (ii) no single transport time scale is valid for all time periods and spatial locations. 

Some thoughts on the concept of residence time (David Jay) 

Residence times are not a single number for a system but they do vary both in space and 

time and are different for different substances. They are a function of the type of system, 

domain bathymetry, tides and various events (hurricanes, floods, etc.). Fjords for 

example, have highly variable residence times in space and time. Some demonstrations 

of the variations of residence times using suspended particulate matter in the Columbia 

river were discussed. 

The CORIE integrated observation and modeling system and its contribution to 

characterizing residual properties and RT (Antonio Baptista, Michela Burla and 

Anabela Oliveira) 

First the CORIE observation network was described and thereafter residence time was 

defined in an Eulerian (flushing based) and Lagrangian (particle path tracking) 

framework with the latter covering both a “once through” and a re-entrant scenario. The 

question “will coastal observations change how we evaluate RT?” was raised and to 

which the answer turned out to be “yes, much yet to be determined”. Finally, the 

accuracy of observations was discussed together with the ensuing residual velocities and 

salinity intrusions. 

 15
Modeling zinc in San Diego Bay (Tom O’Connor) 

Given a known input rate of zinc into San Diego Bay, the zinc concentration in the bay 

was calculated by first assuming complete and total mixing so that zinc was at a uniform 

concentration throughout the bay, regardless of locations of sources. Zinc left the bay 

with the tidal prism and steady state zinc concentration was simply that required for the 

output rate to equal the input rate. Given that the calculated steady state zinc 

concentration was well below water quality criteria the simplifying assumptions may 

have been justified. 

Modeling the fate of copper in San Diego Bay (D. Bart Chadwick, Igancio RiveraDuarte, Alberto Zirino, Amy Blake and Chuck Katz) 

The total copper loading for San Diego bay was described and the balance and fate of 

copper was modeled using a tidally-averaged, 1D box model (non-conservative, steadystate) and a predictive 2D model (non-conservative, non-steady-state). The best results 

for the 1D model were obtained by assuming a uniform settling rate loss configuration. 

The calibrated (against data) 2D model improved the spatial and temporal resolution and 

provided a useful management tool for evaluating changes to copper loading in San 

Diego bay. 

Waste site response and remediation (Lawrence Klein and Jessica White) 

An introduction to the role and responsibilities of the NOS Coastal Protection and 

Restoration Division was given and some of its needs were addressed (better techniques 

for source identification, better prediction of injury and understanding effects of 

dredging, etc.). Thereafter, assessment of injury due to contamination, waste site 

challenges (and how to address them and the information needed to do so) and model 

utilization (and model capabilities and inputs needed – currents, rivers, tides, winds, etc.) 

were discussed. 

Determining estuarine residence/flushing times (Alan Blumberg and Quamrul 

Ahsan) 

Flushing or residence time of an estuarine system can be quantified using two physically 

consistent approaches. They are transport modeling of conservative substances and 

particle tracking. Mathematically these two methodologies are identical. The transport 

modeling approach solves a mass balance equation for a conservative substance, whereas, 

the particle tracking methodology is a Lagrangian approach that tracks the movement of 

individual particles with time. The latter approach has some inherent constraints that lead 

to an adoption of complex treatments of boundary conditions. Other constraints include 

the interpolation methods of velocity at the particle position, the number of particles used 

in the analysis, the role of dispersion, the uncertainty in the analysis and the validation 

process. The complexity in particle tracking modeling has been significantly resolved by 

configuring the methodology in the ECOM (Estuarine and Coastal Ocean Model, a 

derivative of the Princeton Ocean Model) framework. The ECOM model has been the 

model of choice for almost 3000 scientists and engineers during the past 25 years. The 

 16
particle tracking methodology has been adopted by us in modeling the New York/New 

Jersey Harbor Estuary with considerable success. There are primary challenges still to be 

addressed of which the validation of particle path tracking (for realistic simulations) and 

obtaining stable statistics (with a computationally reasonable ensemble particle 

population) are some examples. 

SF6 tracer release experiments (David Ho, Ted Caplow and Peter Schlosser) 

Sulfur hexafluoride (SF6) is an ideal substance to use in tracer experiments because it is 

inexpensive, inert and non-toxic. Some tracer experiments in the Hudson River, Newark 

Bay and East River/Long Island Sound areas were described together with details on the 

injection and measurement techniques. The resulting measurements were compared with 

numerical predictions for the years 2001 and 2003 and residence time estimates were also 

derived and compared between the observed data and the numerical predictions. 

Lagrangian observations of mixing in a stratified estuary (Bob Chant, Rocky Geyer, 

Bob Houghton, Eli Hunter and Jim Lerczak) 

An expression for effective dispersion was derived using a salinity gradient and a salinity 

flux (or a mean velocity times a mean salinity) and it was used to obtain an expression for 

the residence time in an estuary using flux exchange arguments. This expression was 

thereafter applied to a simple channel in order to obtain a residence time value for it in 

terms of the effective dispersion. Experiments in the Hudson River in May 2002 showed 

that the tides were the mixing agent and also that the tidally mean flow did remain 

constant over the neap/spring cycle. Dye experiments yielded the velocity patch 

structure. Together with salinity measurements, it was possible to calculate an effective 

dispersion thereby leading to potential estimations of residence times. 

The impact of the flooding/drying process on the residual time in estuaries 

(Changsheng Chen and Haosheng Huang) 

Several definitions for residence and flushing times were presented with the relatively 

newer dynamical tracer method favored for application in this research. The surface 

residual flow and residual mass were computed after applying the FVCOM model to a 

domain near Broad River, SC where wetting/drying was important. Using the residual 

masses, residence times were computed for two scenarios (with and without inter-tidal 

salt marshes) which leads to the conclusion that the inclusion of the flooding/drying 

process in an estuarine model tended to shorten residence times and hence enhanced the 

water exchange. 

SqueezeBox : Flow-scaled 1D box models for estuary residence time estimates (Joan 

Sheldon and Merryl Alber) 

SqueezeBox is a desktop modeling tool for estimating longitudinal salinity distributions 

and mixing time scales, exploring transport of inert tracers, and evaluating the effects of 

freshwater inflow in riverine estuaries. It generates 1-dimensional, tidally averaged box 

models with structures scalable for different river flows. Scaling the models for 

numerical stability, a step not always included for simple box models, allows them to be 

 17
used for simulations of transient conditions such as those following a pulse input of a 

non-reactive substance (tracer) dissolved in the water. These features allow for estimation 

of a variety of mixing time scales (e.g. transit time and residence times) and for 

investigation of the duration of exposure of estuary segments to introduced substances. 

These types of predictions from SqueezeBox may be useful in interpreting nutrient and 

pollutant dynamics in estuaries or in evaluating the exceedance of water quality 

standards. It could also be used to compare the relative susceptibility of different 

estuaries to perturbations. The modeling framework is flexible, so that new modules can 

be developed independently of the application, and modules have minimal data 

requirements. We have completed modules for two riverine estuaries in Georgia: the 

Ogeechee, a slower-flowing estuary with primarily coastal plain drainage, and the 

Altamaha, a faster-flowing estuary with extensive piedmont drainage. 

Transport analysis using Synoptic Lagrangian Maps (SLMs) : the dynamical 

systems approach (Steve Wiggins, Des Small, Denny Kirwan, Bruce Lipphardt, C. 

E. Grosh and J. Paduan) 

Synoptic Lagrangian Maps (SLMs) encapsulate the spatio-temporal structure of the 

future and/or history of particle trajectories. They are useful when large velocity field 

archives are available, for example velocity vectors on a grid for multiple increments in 

time which could come from either observed data or numerical model predictions. In 

these maps, each particle trajectory is represented by a single pixel, color-coded 

according to its residence time and/or information about its origin/fate. There are many 

kinds of SLMs : forward/backward in time, those containing multiple boundary 

segments, those containing spatio-temporal information, those with 

forward/backward/total residence times, those giving fate location, those giving transport 

pathways, etc. Dynamical systems theory (for example, Lyapunov exponents) helps to 

describe the structures that organize qualitatively different particle trajectories and 

provides the building blocks of the geometric template for Lagrangian transport (for 

example, lobe dynamics which can be used to investigate flow barriers, transport 

alleyways, water mass exchange, etc.). 

Generalized Lagrangian Mean (GLM) theory revisited (John Hamrick) 

Generalized Lagrangian Mean (GLM) theory is an exact theory of wave-mean flow 

interaction and it is an Eulerian mean along a Lagrangian trajectory which is assigned to 

a mean position associated with the trajectory. In GLM theory, quantities are 

mathematically manipulated using Eulerian mean (averaging) operators and the practical 

implementation is usually highly non-linear. For Lagrangian particle path tracking, the 

following sequence of events is adopted : (i) release particles, distributed uniformly in 

space, at numerous intervals over a pre-specified averaging period, (ii) track each particle 

for a period equal to the averaging period, (iii) determine in place the associated mean 

position and velocity of the particle along the trajectory, (iv) average the trajectory mean 

positions and velocities of each particle having the same initial position, (v) locate the 

average velocities at the average position, (vi) interpolate these velocities back to the 

hydrodynamic model grid points, (vii) assume that the form of the weakly non-linear 

GLM continuity is applicable to more non-linear situations, (viii) equate the particle 

tracked GLM plus an error in the form of a scaled potential to the GLM transport, (ix)

 18
clean the divergence from the particle tracking GLM velocity by solving for the scalar 

potential and (x) finally, a GLM transport field results which satisfies an Eulerian form of 

a continuity equation. Therefore, GLM theory has the potential for the Eulerian analysis 

and display of Lagrangian processes. 

 19
Appendix C : Attendees 

Frank Aikman III 

CSDL/NOS/NOAA 

1315 East-West Highway 

Silver Spring, MD 20910 

(301) 713-2809x101 

Frank.Aikman@noaa.gov

Antonio Baptista 

OGI School of Science and Engineering 

Oregon Health and Science University 

20000 NW Walker Road 

Beaverton, OR 97006 

(503) 748-1147 

baptista@ccalmr.ogi.edu

Alan F. Blumberg 

Department of Civil, Environmental & Ocean Engineering 

Stevens Institute of Technology 

Castle Point on Hudson, 

Hoboken, NJ 07030 

(201) 216-5289 

ablumber@stevens.edu

D. Bart Chadwick 

SPAWAR Systems Center San Diego 

Code 2362 

53475 Strothe Road 

San Diego, CA 95152 

(619) 553-5333 

chadwick@spawar.navy.mil

bart.chadwick@navy.mil

Carl Cerco 

US Army Research and Development Center 

Waterways Experiment Station 

3909 Halls Ferry Road 

Vicksburg, MS 39180-6199 

(301) 634-4207 

cercoc@wes.army.mil

Carl.F.Cerco@erdc.usace.army.mil

Bob Chant 

Institute of Marine and Coastal Sciences 

Rutgers University 

 20
71 Dudley Road 

New Brunswick, NJ 08901 

(732) 932-6555 x 544 

chant@marine.rutgers.edu

Changsheng Chen 

School of Marine Science and Technology 

University of Massachusetts - Dartmouth 

706 South Rodney French Boulevard 

New Bedford, MA 02744 

(508) 910-6388 

c1chen@umassd.edu

Edward Dettmann 

EPA/NHEERL 

27 Tarzwell Drive 

Narragansett, RI 02882-1154 

(401) 782-3039 

dettmann.edward@epamail.epa.gov

Jerome Fiechter 

RSMAS – Applied Marine Physics 

4600 Rickenbacker Causeway 

Miami, FL 33149 

(305) 361-4984 

jfiechter@rsmas.miami.edu

Tom Gross 

CSDL/NOS/NOAA 

1315 East-West Highway 

Silver Spring, MD 20910 

(301) 713-2809x139 

Tom.Gross@noaa.gov

John M. Hamrick 

Tetra Tech, Inc. 

10306 Eaton Place, Suite 340, 

Fairfax, VA 22030 

(703) 385-6000 

John.Hamrick@tetratech-ffx.com 

Ferdi Hellweger 

842a Mudd 

Earth & Environmental Engineering 

Columbia University 

New York, NY10027 

(917) 238-3010 

flh23@columbia.edu

 21
David Ho 

Lamont-Doherty Earth Observatory of Columbia University 

Geochemistry Division 

69 Geochemistry 

61 Route 9W – PO Box 1000 

Palisades, NY 10964 

(845) 365-8706 

david@ldeo.columbia.edu

David Jay 

OGI School of Science and Engineering 

Oregon Health and Science University 

20000 NW Walker Road 

Beaverton, OR 97006 

(503) 748-1372 

djay@ebs.ogi.edu

Sung-Chan Kim 

US Army Corps of Engineers 

Engineering Research and Development Center 

Environmental Laboratory 

CEERD-EP-W 

3909 Halls Ferry Road 

Vicksburg, MS 39180 

(601) 634-3783 

Sung-Chan.Kim@erdc.usace.army.mil

Dennis Kirwan 

103 Robinson Hall 

University of Delaware 

Newark DE 19716 

adk@udel.edu

adk@smash.cms.udel.edu

Lawrence Klein 

Associate Coastal Resource Coordinator 

Coastal Protection and Restoration Division 

NOAA/NOS/Office of Response and Restoration 

c/o USEPA (6SF-L), 1445 Ross Avenue 

Dallas, TX 75202-2733 

Lawrence.Klein@noaa.gov

Lyon Lanerolle 

CSDL/NOS/NOAA 

1315 East-West Highway 

Silver Spring, MD 20910 

(301) 713-2809x110 

 22
Lyon.Lanerolle@noaa.gov

Bruce Lipphardt 

104 Robinson Hall 

University of Delaware 

Newark DE 19716 

brucel@udel.edu 

brucel@smash.cms.udel.edu

Daniel G. MacDonald, 

School of Marine Science and Technology 

University of Massachusetts - Dartmouth 

706 South Rodney French Boulevard 

New Bedford, MA 02744 

(508) 910-6334 

dmacdonald@umassd.edu

Reza Malek-Madani 

Research Office, MS 10m 

589 McNair Road 

U. S. Naval Academy 

Annapolis MD 21402 

research@usna.edu

malekmr@onr.navy.mil

Buzz Martin 

The Texas General Land Office 

1700 N. Congress Avenue, Suite 840 

Austin TX 78701 

Buzz.Martin@GLO.STATE.TX.US

Tom O'Connor 

NCCOS/NOS/NOAA 

1305 East-West Highway 

Silver Spring, MD 20910 

(301) 713-3028x151 

Tom.Oconnor@noaa.gov

Bruce Parker 

CSDL/NOS/NOAA 

1315 East-West Highway 

Silver Spring, MD 20910 

(301) 713-2801x121 

Bruce.Parker@noaa.gov

Debbie Payton 

NOAA/NOS/Office of Response and Restoration 

7600 Sand Point Way NE 

 23
Seattle, WA 98115 

(206) 526-6320 

Debbie.Payton@noaa.gov

Hayder Salman 

Mathematics Department 

CB #3250, Phillips Hall 

UNC – Chapel Hill 

Chapel Hill, NC 27599 

(919) 962-1294 

hsalman@email.unc.edu

Richard Schmalz 

CSDL/NOS/NOAA 

1315 East-West Highway 

Silver Spring, MD 20910 

(301) 713-2809x104 

Richard.Schmalz@noaa.gov

Joan Sheldon 

Department of Marine Sciences 

University of Georgia 

Athens, GA 30602 

(706) 542-1283 

jsheldon@uga.edu

Craig Swanson 

Applied Science Associates, Inc. 

70 Dean Knauss Drive 

Narrangansett, RI 02882 

(401) 789-6224 

cswanson@appsci.com

Arnoldo Valle-Levinson 

Center for Coastal Physical Oceanography 

Old Dominion University 

Norfolk, VA 23529 

(757) 683-5578 

arnoldo@ccpo.odu.edu

Glen Watabayashi 

NOAA/NOS/Office of Response and Restoration 

7600 Sand Point Way NE 

Seattle, WA 98115 

(206) 526-6324 

Glen.Watabayashi@noaa.gov

Eugene Wei 

 24
CSDL/NOS/NOAA 

1315 East-West Highway 

Silver Spring, MD 20910 

(301) 713-2809x102 

Eugene.Wei@noaa.gov

Jessica White 

Associate Coastal Resource Coordinator 

Coastal Protection and Restoration Division 

NOAA/NOS/Office of Response and Restoration 

c/o US EPA (6SF-L), 1445 Ross Ave. 

Dallas, Texas 75202-2733 

Jessica.White@noaa.gov

S. R. Wiggins 

Department of Mathematics 

University of Bristol 

University walk 

Clifton 

Bristol BS8 1TW 

United Kingdom 

+44 117 928 7979 

S.Wiggins@bristol.ac.uk 

 25