U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the Operational Science Advisory Team (OSAT3) Steering 

Committee chartered by the Deepwater Horizon Federal On-Scene Coordinator (FOSC)

Application of a Hydrodynamic and Sediment Transport 

Model for Guidance of Response Efforts Related to the 

Deepwater Horizon Oil Spill in the Northern Gulf of Mexico 

Along the Coast of Alabama and Florida

Open-File Report 2012–1234

Application of a Hydrodynamic and 

Sediment Transport Model for Guidance of 

Response Efforts Related to the Deepwater 

Horizon Oil Spill in the Northern Gulf of 

Mexico Along the Coast of Alabama and 

Florida

By Nathaniel G. Plant, Joseph W. Long, P. Soupy Dalyander, David M. Thompson, 

and Ellen A. Raabe

Open-File Report 2012–1234

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

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Suggested citation:

Plant, N.G, Long, J.W., Dalyander, P.S., Thompson, D.M., and Raabe, E.A., 2013, Application of a hydrodynamic and 

sediment transport model for guidance of response efforts related to the Deepwater Horizon oil spill in the northern 

Gulf of Mexico along the coast of Alabama and Florida: U.S. Geological Survey Open-File Report 2012–1234, 48 p., 

http://pubs.usgs.gov/of/2012/1234/.
iii

Contents

Executive Summary.......................................................................................................................................1

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

Overall OSAT3 objectives ....................................................................................................................2

Objectives of USGS Hydrodynamic and Sediment Transport Modeling......................................2

Methods...........................................................................................................................................................3

Modeling Approach..............................................................................................................................3

Hydrodynamic Model Description .....................................................................................................4

Hydrodynamic Model Input Data .......................................................................................................5

Bathymetry....................................................................................................................................5

Waves 6

Winds 6

Tides and Surge............................................................................................................................7

SRB and Sand Movement ...................................................................................................................7

Physical Properties of Sand and SRBs ....................................................................................7

Physical Processes of Sand and SRB Mobility ......................................................................7

Sand and SRB Representative Class Definition .....................................................................8

Inlet Dynamics and Sediment Mobility .............................................................................................8

Metrics for Evaluating Sand and SRB Mobility and Redistribution Patterns ...........................10

Significant Wave Height...........................................................................................................10

Maximum and Median Alongshore Current..........................................................................10

Alongshore Current Convergences ........................................................................................10

Alongshore Current Decelerations.........................................................................................11

Sand and SRB Mobility Ratio...................................................................................................11

SRB Surf-Zone Integrated Alongshore Potential Flux.........................................................12

Weighted Mobility Probability .................................................................................................12

Weighted Potential Flux............................................................................................................12

Tidal Mobility...............................................................................................................................12

Tidal Inlet Animations.........................................................................................................................12

Results13

Model Evaluation ................................................................................................................................13

Wave Model................................................................................................................................13

Tide and Storm Simulations......................................................................................................15

Scenario Simulation Results.............................................................................................................16

Scenario Analysis......................................................................................................................17

SRB and Sand Weighted Mobility Probability and Potential Flux......................................21

Tidal-Inlet Time-Series Results................................................................................................21

Discussion.....................................................................................................................................................21

Implications of Results for Understanding SRB Formation, Burial, Exhumation, and

Transport.................................................................................................................................21

Alongshore-Currents and Gradients in Transport................................................................24

Inlet Dynamics............................................................................................................................24

Complexity of Coupled SRB and Sand Dynamics.................................................................25
iv

Effect of Assumptions ........................................................................................................................25

Scenario Selection ....................................................................................................................25

SRB Size, Shape, and Exposure ..............................................................................................25

Focus on Alongshore Processes ............................................................................................26

Static Bathymetry ......................................................................................................................27

Accuracy of Boundary Conditions..........................................................................................27

Research Gaps....................................................................................................................................27

Future Research Opportunities ...............................................................................................28

Operational Applications of Results and Methods ..............................................................28

Summary And Conclusions ........................................................................................................................29

References Cited..........................................................................................................................................29

Appendix 1. Scenarios.............................................................................................................................33

Appendix 2. Examples of Input Files for the Model ............................................................................37

Appendix 3. Calculations of Mobility and Potential Flux....................................................................44

Appendix 4. File Naming Conventions ..................................................................................................46

Appendix 5. Time Step of Maximum Ebb and Flood for Inlets in the Model Domain ....................47

Figures

1. OSAT3 model domain within the northern Gulf of Mexico and showing

bathymetry .....................................................................................................................................3

2. Schematization of wave height and direction observations from NDBC buoy 42040

for April 1, 2010, to May 1, 2012 ..................................................................................................4

3. Generation of alongshore currents due to wave breaking at an angle to the Gulf

coast of Alabama and Florida.....................................................................................................5

4. Modeled wave height from the H5_D7 scenario simulation and associated wavedriven current vectors showing resolution of the cross-shore variable alongshore 

current profile................................................................................................................................5

5. Elevations (NAVD88) at three levels of detail for Little Lagoon Inlet, Ala ...........................6

6. Distribution of surface residual ball density (ρ) calculated from chemical

composition along the Alabama and Florida Gulf coast ........................................................8

7. Processes driving surface residual ball and sediment mobility and transport

along the Alabama and Florida Gulf coast ...............................................................................8

8. Critical shear stress (in Pa) of surface residual balls along the Alabama and

Florida Gulf coast as a function of diameter............................................................................9

9. Critical stress of sand and surface residual balls along the Alabama and Florida 

Gulf coast, after Shields (1936) shown as a function of density and grain size for 

six particle sizes............................................................................................................................9

10. Two mechanisms of increased probability for surface residual ball accumulation .......11

11. NDBC directional wave buoys (42012, 42039, and 42040) and a Naval Research

Laboratory acoustic doppler current profiler used for model evaluation along the 

Alabama and Florida Gulf coast...............................................................................................13

12. Comparison of Wavewatch III and SWAN model output to significant wave height

and wave period observations at NDBC buoy 42012 between May 1, 2010, and 

May 1, 2011 ..................................................................................................................................14
v

13. Model predictions of wave height and wave direction from the 80 scenarios compared

with observations at NDBC buoy 42012 in the northern Gulf of Mexico alongshore

Alabama and Florida ..................................................................................................................15

14. Model predictions of wave height, peak wave direction and peak wave period in

the northern Gulf of Mexico alongshore Alabama and Florida for January 15–25, 

2007 ...............................................................................................................................................16

15. Evaluation of accuracy of simulated water levels against NOAA tidal 

measurements ............................................................................................................................16

16. Simulated and measured wave characteristics at buoy 42012 in the northern 

Gulf of Mexico alongshore Alabama and Florida during Hurricane Isaac in 

August 2012..................................................................................................................................17

17. Simulation of water levels in the northern Gulf of Mexico alongshore Alabama 

and Florida during Hurricane Isaac in August 2012 compared with measured 

water level at the NOAA tide stations.....................................................................................17

18. Significant wave height for scenarios H3_D6 and H3_D8 in the northern Gulf of

Mexico alongshore Alabama and Florida...............................................................................18

19. Maximum alongshore velocity smoothed over a 2-kilometer length scale for

scenarios H3_D6 and H3_D8 in the northern Gulf of Mexico alongshore 

Alabama and Florida ..................................................................................................................18

20. Flow convergence for scenarios H3_D6 and H3_D8 in the northern Gulf of 

Mexico alongshore Alabama and Florida...............................................................................19

21. Flow deceleration for scenarios H3_D6 and H3_D8 in the northern Gulf of 

Mexico alongshore Alabama and Florida...............................................................................19

22. Mobility ratio in the northern Gulf of Mexico alongshore Alabama and Florida for 

a midlevel threshold of 2.5-centimeter surface residual balls for scenarios H3_D6

and H4_D6....................................................................................................................................20

23. Mobility ratio in the northern Gulf of Mexico alongshore Alabama and Florida for

sand for scenarios H3_D6 and H4_D6.....................................................................................20

24. Mobility ratio in the northern Gulf of Mexico alongshore Alabama and Florida for 

a midlevel threshold of 2.5-centimeter surface residual balls along the Gulf Islands

National Seashore......................................................................................................................21

25. Surf-zone integrated alongshore potential flux smoothed over 2 kilometers for

2.5-centimeter surface residual balls in the northern Gulf of Mexico alongshore

Alabama and Florida ..................................................................................................................22

26. Weighted mobility probability from April 2010 to May 2012 along the Gulf Islands 

National Seashore for 2.5-centimeter surface residual balls .............................................22

27. Weighted surf-zone integrated alongshore potential flux, indicating the average 

potential flux in the northern Gulf of Mexico alongshore Alabama and Florida from 

April 2010 to May 2012 ...............................................................................................................23

28. Tidal inlet surface residual ball mobility at maximum flood and maximum ebb for 

2.5-centimeter SRBs using a low critical threshold at Little Lagoon Inlet, Ala................23

29. Maximum alongshore flow speed smoothed over a 2-kilometer length scale and 

mobility ratio using the lowest critical stress threshold, appropriate for surface 

residual balls ...............................................................................................................................24

30. Morphologic features at the Pensacola Inlet, Fla., that interact with the tidal flow.......25

31. Mobility ratios of 0.03-centimeter quartz sand (sediment); and 2.5-cm and 10-cm 

surface residual balls under large wave conditions in the northern Gulf of Mexico......26

32. Observed wave height at the Naval Research Labortory acoustic dopler current 
vi

profiler in the northern Gulf of Mexico alongshore Alabama and Florida for 

September 15, 2006, through December 23, 2007..................................................................26

1–1. Example of a scenario H3_D8 with wave height of 1.25 meters and wave direction 

of 169 degrees .............................................................................................................................35

1–2. Comparison of the best-match condition to the target values for the scenario 

against all observations for scenario H3_D8 .........................................................................36

Tables

1. Classes of surface residual ball size and density considered in mobility, potential

flux analysis, and critical stress in the northern Gulf of Mexico alongshore

Alabama and Florida ..................................................................................................................10

2. Nine metrics for hydrodynamic and surface residual ball and sediment mobility and

alongshore redistribution in the northern Gulf of Mexico along the Alabama and

Florida coast................................................................................................................................11

3. Comparison of high resolution SWAN model output to Wavewatch III model output,

evaluated against observed buoy data from May 1, 2010, to May 1, 2011 ........................14

4. Comparison of Wavewatch III model output to data from three northern Gulf of

Mexico offshore NDBC buoys for the 2-year time period of from May 1, 2010, to

May 1, 2012 ..................................................................................................................................15

1–1. Wave height and direction scenarios .....................................................................................33

5–1. Time step index corresponding to maximum flood and ebb for inlets within the

model domain ..............................................................................................................................47
vii

Conversion Factors, Datum, and 

Abbreviations

SI to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square kilometer (km2

) 247.1 acre

square meter (m2

) 10.76 square foot (ft2) 

Volume

cubic meter (m3

) 264.2 gallon (gal) 

cubic meter (m3

) 35.31 cubic foot (ft3)

Flow rate

meter per second (m/s) 3.281 foot per second (ft/s) 

cubic meter per second (m3

/s) 35.31 cubic foot per second (ft3/s)

Mass

kilogram (kg) 2.205 pound avoirdupois (lb)

Pressure

kilopascal (kPa) 0.1450 pound-force per inch (lbf/in) 

Density

kilogram per cubic meter (kg/m3

) 0.06242 pound per cubic foot (lb/ft3) 

Hydraulic conductivity

meter per day (m/d) 3.281 foot per day (ft/d) 

Hydraulic gradient

meter per kilometer (m/km) 5.27983 foot per mile (ft/mi) 

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the World Geodetic System of 1983 (WGS 83).

Elevation, as used in this report, refers to distance above the vertical datum.
viii

Abbreviations

Term Definition

ADCP acoustic doppler current profiler

BP British Petroleum

CO-OPS Center for Operational Oceanographic Products and Services

DOI U.S. Department of the Interior

EMC Environmental Modeling Center

FOSC Deepwater Horizon Federal On-Scene Coordinator

GCRO Gulf Coast Restoration Organization

HYCOM Hybrid Coordinate Ocean Model

JONSWAP Joint North Sea Wave Project 

NCEP National Center for Environmental Prediction

NDBC National Data Buoy Center

NGDC National Geophysical Data Center

NOAA National Oceanic and Atmospheric Administration

NRDA Natural Resource Resource Assessment

NRL Naval Research Laboratory

NWS National Weather Service

OSAT3 Operational Science Advisory Team

R2 coefficient of determination 

RMSE root mean square error

SRB surface residual balls

SWAN Simulating Waves Nearshore

USACE U.S. Army Corps of Engineers

USCG U.S. Coast Guard

USGS U.S. Geological Survey
Application of a Hydrodynamic and Sediment Transport 

Model for Guidance of Response Efforts Related to the 

Deepwater Horizon Oil Spill in the Northern Gulf of 

Mexico Along the Coast of Alabama and Florida

By Nathaniel G. Plant, Joseph W. Long, P. Soupy Dalyander, David M. Thompson, and Ellen A. Raabe

Executive Summary

U.S. Geological Survey (USGS) scientists have provided 

a model-based assessment of transport and deposition of 

residual Deepwater Horizon oil along the shoreline within the 

northern Gulf of Mexico in the form of mixtures of sand and 

weathered oil, known as surface residual balls (SRBs). The 

results of this USGS research, in combination with results 

from other components of the overall study, will inform operational decisionmaking. The results will provide guidance for 

response activities and data collection needs during future oil 

spills.

In May 2012 the U.S. Coast Guard, acting as the 

Deepwater Horizon Federal on-scene coordinator, chartered 

an operational science advisory team to provide a sciencebased review of data collected and to conduct additional 

directed studies and sampling. The goal was to characterize 

typical shoreline profiles and morphology in the northern 

Gulf of Mexico to identify likely sources of residual oil and 

to evaluate mechanisms whereby reoiling phenomena may be 

occurring (for example, burial and exhumation and alongshore transport). A steering committee cochaired by British 

Petroleum Corporation (BP) and the National Oceanic and 

Atmospheric Administration (NOAA) is overseeing the project 

and includes State on-scene coordinators from four States 

(Alabama, Florida, Louisiana, and Mississippi), trustees of 

the U.S. Department of the Interior (DOI), and representatives 

from the U.S. Coast Guard.

This report presents the results of hydrodynamic and 

sediment transport models and developed techniques for 

analyzing potential SRB movement and burial and exhumation along the coastline of Alabama and Florida. Results 

from these modeling efforts are being used to explain the 

complexity of reoiling in the nearshore environment and to 

broaden consideration of the different scenarios and difficulties that are being faced in identifying and removing residual 

oil. For instance, modeling results suggest that larger SRBs 

are not, under the most commonly observed low-energy wave 

conditions, likely to move very far alongshore. This finding 

suggests that SRBs from one source location may not (outside 

of storm conditions) be redistributed to other up or down coast 

locations. This information can guide operational response 

decisions. In addition, because SRBs are less mobile compared 

with sand, they are likely to become buried and unburied 

under normal sand transport processes thereby lengthening 

the time SRBs may take to move onshore. The rate of onshore 

movement was not specifically addressed by this study, yet the 

results resolve the cross-shore domain and cross-shore variations in alongshore transport that are relevant to achieving the 

primary objectives. Furthermore, during infrequent events (for 

example, winter storms and severe meteorological events such 

as Hurricane Isaac of August 2012), energy is shown to be 

sufficient to move a greater range of SRB sizes and potentially 

expose and break up submerged oil mats. When SRBs do 

move alongshore, the models indicate that there are regions 

that are more conducive to accumulation of SRB material than 

others. Accumulation can occur where there are reversals and 

decelerations in alongshore currents and where forces created 

by shear stress drops below critical thresholds to maintain or 

initiate SRB movement. In addition, flow and SRB mobility 

patterns around inlets indicate patterns in hydrodynamic forces 

that influence redistribution of SRBs and the surface oil that 

mixed with sediment to form oil mats in the first place.

Introduction

Source, transport, and deposition of residual Deepwater 

Horizon oil that is causing shoreline reoiling along the 

coastlines of Alabama, Florida, Louisiana, and Mississippi 

is not well understood, and existing scientific knowledge 

has proven insufficient to fully support cleanup response 

and management decisions. Therefore, in May 2012, the 

U.S. Coast Guard, acting as the Federal On-Scene Coordinator chartered the third Operational Science Advisory Team 

(OSAT3) to provide science-based review of data collected 
2 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

(for example, morphologic elevations and oiling locations) 

and to conduct additional directed studies and sampling 

as necessary. A steering committee cochaired by British 

Petroleum Corporation (BP) and the National Oceanic and 

Atmospheric Administration (NOAA) is overseeing the project 

and includes State on-scene coordinators from four States 

(Alabama, Florida, Louisiana, and Mississippi), trustees of 

the U.S. Department of the Interior (DOI), and representatives 

from the U.S. Coast Guard.

Residual oil from the Deepwater Horizon spill is found 

in the shallow surf-zone in the northern Gulf of Mexico in 

two primary forms: submerged oil mats and surface residual 

balls (SRBs). Mats formed when weathered oil at the surface 

reached a shallow, energetic-enough location for wave-stirred 

sediment to mix with the oil and create a sand and oil mixture. This mixture can become heavier than water and settle 

to the the sea floor where more sediment can be incorporated, 

forming a submerged mat. Mats encountered as part of the 

Deepwater Horizon response efforts are generally meters 

in cross-shore width, meters to tens of meters in alongshore 

length, and a few to tens of centimeters thick. Under sufficiently energetic wave conditions, buried mats can be 

exhumed and pieces of the mats can break off and form SRBs 

(Shoreline Cleanup and Assessment Team, oral commun., 

2012). The SRBs are observed in the surf zone and may wash 

up on beaches. SRBs and mats in the surf zone and on the 

beach are targets of ongoing cleanup response efforts. This 

report presents the results of an OSAT3 subgroup that developed hydrodynamic and sediment transport models and developed techniques for analyzing potential SRB redistribution 

and burial and exhumation to provide a better understanding 

of alongshore processes and movement of SRBs along the 

coastline of Alabama and Florida.

Overall OSAT3 objectives

To provide improved understanding and guidance in 

support of the operational response to shoreline reoiling, 

OSAT3 undertook five main tasks:

• Evaluate the trends observed in frequency, rate, and 

potential for remobilization on beach segments in the 

areas affected by reoiling.

• Determine and record the locations and typical shoreline profiles and morphology for likely sources of 

residual oil or origin of the SRBs.

• Define or determine the mechanisms whereby reoiling 

phenomena may be occurring.

• Investigate the potential for mitigation actions that may 

be taken to reduce these potential occurrences and, to 

the extent reoiling phenomena are identified, evaluate 

the feasibility of the mitigation actions and net environmental benefit of employing such actions.

• Recommend a path forward to reach shoreline cleanup 

completion plan guidelines or appropriately manage 

identified areas through alternative methods.

To achieve these overall objectives, the OSAT3 

subgroup collected and analyzed shoreline cleanup data (for 

example, SRB and mat recovery records and photographs 

showing location and size of SRBs) and geomorphic data 

(beach profiles, aerial imagery, shorelines, topography, and 

bathymetry) and conducted numerical modeling analysis of 

waves, water levels, currents, and local surficial sediment, and 

SRB mobility and transport. This report specifically addresses 

the numerical modeling aspect of the OSAT3 objectives along 

the coastline of Alabama and Florida; overall OSAT3 findings 

are not within the scope of the analysis of this report.

Objectives of USGS Hydrodynamic and 

Sediment Transport Modeling

This report documents the approach, results, and conclusions from the USGS OSAT3 subgroup that developed 

hydrodynamic and sediment (including SRBs) transport 

models to provide better understanding and prediction of 

alongshore processes and movement of SRBs. The subgroup 

was split into two teams tasked with analyzing specific regions 

of the affected coastline. One team covered the Louisiana and 

Mississippi coastlines (results not presented in this report), and 

the other team covered the Alabama and Florida coastlines. 

The latter region was modeled by researchers from the USGS 

Coastal and Marine Geology Program. The specific objectives 

of this subgroup’s effort were to:

• identify spatial patterns in alongshore current directions and velocity;

• identify zones of convergence and alongshore current 

reversal;

• identify potential sediment and SRB sinks;

• estimate SRB movement along the coast; and, 

• determine the influence of tidal currents on SRB 

mobility and transport in the vicinity of tidal inlets.

These objectives were achieved through modeling 

scenarios covering the range of weather and wave variability 

since the Deepwater Horizon spill; extracting wave-driven 

alongshore currents, wave-orbital stirring, and tidal currents; 

and computing associated sediment and SRB mobility and 

alongshore transport patterns. The approach to selecting 

scenarios, hydrodynamic modeling, and SRB mobility and 

transport modeling is described in the Methods section. In the 

Results section, the modeled hydrodynamics are evaluated 

against observations and the alongshore current and SRB 

transport results from the scenarios are described. The impact 

of the results on achieving the overall OSAT3 objectives 

is described in the Discussion section. An analysis of our 

assumptions along with implications of our methods and 
Methods 3

findings for future operations associated with reoiling response 

are also discussed. The major findings from this study are 

summarized in the Conclusions section.

Methods

The coastline of interest included in our analysis stretches 

from Dauphin Island, Ala. to Panama City Inlet, Fla. The 

domain for our entire OSAT3 model encompasses a wider 

stretch of coast from Horn Island, Miss. to Crooked Island, 

Fla. (fig. 1) to ensure that the regions of interest in Alabama 

and Florida were not affected by the lateral boundaries of the 

domain for the model. The curvilinear model grid resolution 

was variable with an average alongshore resolution of 250 

meters (m) and a cross-shore grid spacing ranging from 150 

m far offshore to 2.5 m near the shoreline. The size of the 

model domain allowed the inclusion of large-scale variations 

in wind and wave patterns, and the increased resolution in the 

nearshore allowed for computation of finer scale surf zone 

processes driven by depth-induced wave breaking. Computational efficiency was achieved with the variable grid spacing. 

This domain was nested within global and basin-scale wave 

and hydrodynamic model domains encompassing at a minimum the entire Gulf of Mexico in order to derive adequate 

spatially varying boundary conditions to drive processes in the 

OSAT3 model domain.

Figure 1. OSAT3 model 

domain within A, the northern 

Gulf of Mexico and B, showing 

bathymetry. Colors in B

represent water depths relative 

to the North American Vertical 

Datum of 1988 (NAVD88). 

Analysis of model results 

extends from Dauphin Island, 

Ala., to Panama City Inlet, Fla.

Modeling Approach

Hydrodynamic simulations included scenarios derived 

from wave and weather observations at the National Data 

Buoy Center (NDBC; 2012) buoy 42040 from April 1, 2010, 

to May 1, 2012. This buoy was just offshore of the eastern side 

of the OSAT3 model domain. The wave observations were 

schematized by dividing wave heights into 5 bins bounded by 

0.0, 0.5, 1.0, 1.5, 2.0, and 5.0 m and sampling wave directions 

in 16 bins each spanning 22.5 degrees (°), from 0° to 360°. 

The combination of wave height and direction bins yielded 

80 different scenarios. The probability of occurrence of each 

scenario (fig. 2) indicated that waves were most likely to have 

heights of 0.5 to 1.0 m and come from the southeast. However, 

the set of scenarios that were considered included common 

and relatively rare wave conditions. The details of selecting 

scenarios are described in appendix 1.

Due to the large geographic extent and variability of 

the model domain, application of spatially homogeneous 

wave conditions along the entire offshore model boundary 

would provide unrealistic results. Therefore, for each of 

the scenarios, the observed wave record was searched for a 

specific time that most closely matched the characteristics of 
4 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

the scenario. Then, archived results from the National Weather 

Service (NWS) National Center for Environmental Prediction 

(NCEP) NOAA Wavewatch III regional wave model 

(Environmental Modeling Center, 2012), corresponding to 

that specific time, were applied to the OSAT3 model domain 

boundaries. Archived winds from the same regional model, 

also corresponding to the same point in time, were applied to 

the free-surface boundary of the entire OSAT3 model domain. 

Stationary wave conditions were used and variations in water 

level were not considered for the scenario simulations.

In addition to the stationary scenarios, two time periods 

were simulated to evaluate model accuracy over a range 

of conditions: (1) January 15–25, 2007, which included 

both quiescent and storm conditions during winter and 

(2) Hurricane Isaac on August 27–31, 2012, an extreme 

weather event during summer. For these simulations, timevarying wave conditions were imposed on the boundaries of 

the OSAT3 model.

Figure 2. Schematization 

of wave height and direction 

observations from NDBC 

buoy 42040 for April 1, 2010, to 

May 1, 2012. Colors indicate 

the percentage (%) of the 

occurrence for each wave 

height-direction bin. Wave 

height bins (numbered H1–H5) 

are organized from the center 

outward with larger waves 

(2 m and higher) in the outer 

ring (H5). Wave direction bins 

(numbered D1–D16) each 

span 22.5 degrees (°), from 0° 

to 360°, labeled around the 

circumference of the diagram.

Hydrodynamic Model Description

We used the Delft3D (version 4.00.01) coupled waveflow model to compute stirring associated with wave orbital 

velocities and steady wave and wind-driven alongshore 

currents (Lesser and others, 2004; Deltares, 2007). The model 

computes flow variables using the depth-averaged shallow 

water equations that are intrinsically relevant to analyzing 

alongshore currents in the domain, particularly in the surf 

zone. We used model parameter values that have been demonstrated in Lesser and others (2004) to be appropriate for 

the sandy coastlines similar to those within our project area. 

Model parameters are documented in appendix 2 as part of the 

example input files for the Flow and Wave modules.

Three-dimensional surf zone processes were not simulated due to the focus on the prediction and role of alongshore 

currents (as opposed to cross-shore processes) in transporting 

SRBs along the project domain. In the nearshore environment, 

currents are caused primarily by wave-breaking processes. 

Reniers and others (2004) showed that vertical profiles of 

wave-driven alongshore currents are relatively depth-uniform, 

indicating that the use of depth-averaged models is acceptable. 

Density stratification was also assumed to be negligible due 

to intense vertical mixing by breaking waves and stratification 

was not included in the model equations. Winds are included 

in the model to generate waves within the domain. Although 

currents caused by wave breaking processes are dominant in 

the nearshore environment, the model also simulates currents 

generated by wind blowing over the ocean surface. Variable 

water depth and its influence on wave refraction, shoaling, and 

breaking and alongshore current magnitude and location was 

included.
Methods 5

Alongshore current directions and magnitudes (for 

example, eastward or westward following the curvature of 

the model grid) were required to understand the movement of 

sediments and SRBs under various wave conditions. Waves 

approaching the shoreline at an angle break and transfer their 

momentum to the water column, creating the primary force 

that is responsible for driving alongshore currents (fig. 3). 

Generally, waves approaching from the west drive currents 

to the east and vice versa. Depending on the local geometry 

Figure 3. Generation of alongshore currents due to wave 

breaking at an angle to the Gulf coast of Alabama and Florida. 

Image used with permission (COMET® Website, 2011).

of the coast and nearshore bathymetry, complex spatial patterns in the magnitude and direction of the alongshore current 

can develop. The cross shore and alongshore variations of 

the nearshore currents were resolved with the model grid 

and depict the alongshore current jet that is driven by wave 

breaking near the shoreline (fig. 4).

Hydrodynamic Model Input Data

Bathymetry

Bathymetric data (fig. 1) were obtained from the northern Gulf Coast digital elevation map of the NOAA National 

Geophysical Data Center (NGDC; Love and others, 2012). 

These data, with 30-m resolution, satisfied the large-scale 

needs of the OSAT3 domain. An exception was at Little 

Lagoon Inlet, Ala., which, at 10 m wide, required higher grid 

resolution and more accurate bathymetric data (fig. 5A) to 

define the inlet for simulations, including tidal variations. 

Refined inlet resolution was not used in the scenario simulations where temporal water level variations were not considered. At Little Lagoon, we used data from the U.S. Army 

Corps of Engineers (USACE, 2010) collected in January 

through March 2010, just before the Deepwater Horizon oil 

spill (fig. 5B). Additionally, for the Little Lagoon Inlet, we 

assimilated stereoelevation data collected as part of the spill 

response (Aero-Metric, Inc., unpub. data, 2012) to improve 

simulation results, determine the sensitivity of modeled flows 

Figure 4. A, Modeled wave 

height from the H5_D7 scenario 

simulation (fig. 2; wave 

height more than 2 m from 

the southeast); B, associated 

wave-driven current vectors 

showing resolution of 

the cross-shore variable 

alongshore current profile 

(arrow length is proportional 

to current speed). The number 

of current vectors has been 

reduced by a factor of six in the 

cross-shore direction in B for 

better viewing. Color gradation 

near the coast in B illustrates 

depth-induced wave breaking 

in shallow water depths.
6 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Figure 5. Elevations (NAVD88) at three levels of detail for Little 

Lagoon Inlet, Ala. A, 30–m resolution digital elevations (Love and 

others, 2012); B, 1-m resolution lidar elevations (USACE, 2010); and 

C, fall 2012 2-m resolution stereoanalysis elevations (Aero-Metric, 

Inc., unpub. data, 2012). Elevations are posted on the model grid to 

illustrate the increased resolution at the inlet.

to bathymetric changes, and demonstrate an ability to integrate 

this relatively novel data source (fig. 5C).

Geomorphic features larger than the smallest grid cells 

of the model (that is, 250 m in the alongshore and 10 m in 

the cross-shore) were resolved in the model. Thus, nearshore 

features such as sandbars, mega cusps, and other features 

relevant to this effort were evaluated. These nearshore 

features, however, are highly ephemeral, and temporal variations were not resolved over the approximately 2-year time 

period that the simulations represented. Lidar or stereometric 

observations (fig. 5B, C) near Little Lagoon represented more 

recent and accurate snapshots of bathymetric variation. Large 

offshore features such as submarine canyons that can affect the 

wave climate were spatially resolved by the models providing 

boundary conditions to the domain use in our modeling 

simulations.

Waves

Archived results from the NOAA Wavewatch III operational 4-minute (‘), or about 7.5-kilometer (km) resolution 

U.S. East Coast and Gulf of Mexico wave model (Tolman, 

2008; Environmental Modeling Center, 2012) were used for 

the boundary conditions in the Wave module of Delft3D. This 

wave model is part of a nested series of operational models 

of varying sizes and resolutions that extend to a global-scale 

parent grid. The model system has been run, essentially in 

the stated configuration, since February 2005, and NOAA 

provides archives of bulk wave parameters at 3-hour intervals 

from modeled hindcasts. Wave heights, periods, and directions 

from Wavewatch III were extracted and prescribed along 

the offshore and lateral boundaries of the OSAT3 domain 

with an assumed Joint North Sea Wave Project (JONSWAP) 

spectral shape (Hasselmann and others, 1973). The boundary 

conditions were prescribed at every thirtieth grid cell, matching the coarse resolution of the Wavewatch III model. Wave 

conditions for the scenario simulations were held stationary. 

For the time series simulations, wave conditions were updated 

every 3 hours. The directional domain for the wave model 

covered a full circle with a resolution of 5° (72 bins in total), 

and the frequency domain was 0.05 to 1 hertz (Hz) with logarithmic spacing. The bottom-friction dissipation parameterization of Hasselmann and others (1973) was used with a uniform 

bottom roughness coefficient of 0.067 square meters per 

second cubed (m2

/s3). Additionally, so-called third-generation 

physics were activated, accounting for wind wave generation, 

triad wave interactions, and white capping by the Komen and 

others (1984) parameterization. Depth-induced wave breaking 

dissipation was included using the Battjes and Janssen (1978) 

parameterization with default values for alpha (1) and gamma 

(0.73). More details regarding input parameters can be found 

in the Wave input file in appendix 2.
Methods 7

Winds

Wind velocities were also obtained from the archived 

Wavewatch III 4′-resolution data. NOAA uses winds from 

their Global Forecast System weather model to generate waves 

in Wavewatch III and stores this wind data in the Wavewatch 

III archives (Environmental Modeling Center, 2012). These 

wind velocities were extracted from the archives and applied 

over the entire OSAT3 model domain. As done for the waves, 

the wind velocities for the scenario simulations were held stationary whereas for the time series simulations wind velocities 

were updated every 3 hours.

Tides and Surge

Variations in water levels were accounted for in the timeseries simulations. Water levels imposed at the model boundaries were obtained from the TPXO7.2 global tide model 

which uses a numerical tidal model and satellite-derived 

observations of tide elevation to produce tidal constituents 

(Egbert and Erofeeva, 2010). Subtidal water level fluctuations 

that accounted for regional oceanographic processes were 

obtained from a large-scale ocean model (Hybrid Coordinate 

Ocean Model, 2012a) that simulated tides and surge within 

the Gulf of Mexico with a resolution of approximately 4 km. 

Hybrid Coordinate Ocean Model (HYCOM; 2012b) data 

assimilation incorporates observations of water level derived 

from satellite altimeters, which increases prediction accuracy. 

Hourly water level variations from the combination of tidal 

and subtidal water level models were imposed at the two offshore corners of the domain and linearly interpolated along the 

offshore boundary. Spatially varying tidal flows into and out 

of the inlets and estuaries along the project site were included 

and evaluated in time series simulations.

SRB and Sand Movement

The goal of assessing SRB response to hydrodynamic 

conditions is split into determining the likelihood of SRBs to 

move (thresholds for incipient motion, for example, mobility, 

are exceeded), the likelihood to be buried or exhumed by surrounding sediment, the propensity for alongshore transport, 

and the tendency to accumulate. SRB burial and exhumation 

are more likely in areas of more mobile sediment, particularly 

where sand is mobile and SRBs are immobile. The types of 

analysis conducted for each scenario and time-series, therefore, were SRB mobility, local surficial sediment mobility, 

and SRB potential flux, which was used as a proxy to identify 

probable alongshore patterns in SRB redistribution. The exact 

velocity and alongshore transport distances of individual SRBs 

could not be assessed because the locations of SRBs or their 

sources are unknown. We are also limited by some fundamental uncertainties about SRB transport (see Discussion section).

Physical Properties of Sand and SRBs

The response of sand and SRBs to hydrodynamic forces 

is a function of the size and density of the particles. For sediment (without oil), the median grain size in the surf zone in 

this region was determined to vary between 0.250 and 0.500 

millimeters (mm; D.C. Phelps and others, Florida Geological 

Survey, unpub. data, 2011). Sand in this region was predominantly quartz (Balsam and Beeson, 2003) and therefore 

of approximately 2,650-kilogram per cubic meter (kg/m3) 

density. Quantitative information on SRB chemical composition came from an OSAT-supplied dataset (L. Bruce, British 

Petroleum Corporation, Gulf Coast Restoration Organization 

(GCRO), Science Natural Resource Damage Assessment Team 

(NRDA), unpub. data, 2012) and was used to calculate the 

variability in density (fig. 6; appendix 3). Observational data 

on the size distribution of SRBs were not available, therefore a 

range of classes (0.03 centimeters (cm), 0.5 cm, 1 cm, 2.5 cm, 

5 cm, and 10 cm) were chosen to span the estimated range of 

SRB size variability (W. Bryant, U.S. Geological Survey, oral 

commun., 2012).

Physical Processes of Sand and SRB Mobility

The processes that were considered in the SRB and sediment mobility and transport analysis included stirring due 

to wave orbital motion at the sea floor, alongshore currents, 

and tidal currents at inlets (fig. 7). SRBs or sand grains will 

begin to move when the shear stress force associated with the 

combined action of waves and currents exceeds a size- and 

density-specific critical threshold value. See appendix 3 for 

calculation of shear stress from hydrodynamic results and 

calculation of critical stress thresholds. Localized turbulence 

and wave-to-wave variation can cause any individual particle 

to move at calculated stress values below threshold; however, 

the formulations used here, on average, have been found to be 

accurate for surf zone calculation (Deigaard and others, 1991; 

Soulsby and others, 1993).

Critical stress values could also be affected by particle 

shape and exposure above the sea floor. The empirical mobility 

relationship originally developed by Shields (1936) and used 

in this analysis is for a uniform bed of well-packed sediment, 

and larger particles such as SRBs extruding above the bed 

would have a lower critical value for mobility than estimated 

with the standard Shields calculation (Fenton and Abbott, 

1977; Andrews, 1983; Wiberg and Smith, 1987; Wilcock, 

1998; Bottacin-Busolin and others, 2008). Because individual 

SRBs may have varying exposure above the surrounding sea 

floor, three critical stress values were considered to account 

for departures from the simple assumption in Shields (1936). 

The high critical stress values recorded during the study 

would be the ones required to move unexposed SRBs sitting 

approximately level with the surrounding bed, such as might 

be expected in a recently fragmented mat. The medium critical 

stress values correspond to a partially exposed SRB, and the 

low critical stress values correspond to a single isolated SRB 
8 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

fully exposed atop on the sea floor (appendix 3). The medium 

and low critical stress values for any given particle are roughly 

a third and a sixth of the high critical stress estimate (fig. 8). 

Local surficial sediment mobility was assessed using a single 

critical stress value based on the Shields parameterization or 

the high estimate for SRBs because the sand in the northern 

Gulf of Mexico surf zone is of generally uniform size.

Figure 6. Distribution of 

surface residual ball (SRB) 

density (ρ) calculated from 

chemical composition along 

the Alabama and Florida Gulf 

coast. Data are from L. Bruce, 

British Petroleum Corporation, 

GCRO, Science/NRDA Team 

(unpub. data, 2012). 

Figure 7. Processes driving surface residual ball (SRB) and 

sediment mobility and transport along the Alabama and Florida 

Gulf coast. Wave- and current-induced shear stress can 

resuspend sand, SRBs, and other material from the sea floor, 

leading to potential transport by currents. (Symbols used by 

permission from Integration and Application Network, 2012).

Sand and SRB Representative Class Definition

To estimate the mobility and potential flux associated 

with the modeled waves and currents, SRB or local sediment 

diameter and density must be specified. Particle density is well 

constrained for the predominantly quartz sand in this region 

but varied somewhat for observed SRBs. The sensitivity of 

the critical stress required for inducing particle mobility was 

examined for a range of densities consistent with SRB data. 

The variations in SRB density caused relatively small critical 

stress variations compared with the differences due to variations in SRB size and in comparison sand mobility (fig. 9). 

Thus, particle diameter was the dominant control on mobility 

(figs. 8 and 9). Therefore, overall SRB variability was characterized by a set of six classes of varying size and fixed density. 

Local sediment was characterized by a single size and density 

(table 1).
Methods 9

Figure 8. Critical shear stress (in Pa) of surface residual balls (SRBs) along the Alabama and Florida Gulf coast as a function of 

diameter (in cm). Shown are values calculated using the original Shields (1936) formulation, and a modified version accounting for 

exposure wherein the dimensionless sheer stress approaches a constant value for particles that are partially exposed (0.1) or fully 

exposed (0.2; see appendix 3).

Figure 9. Critical stress of 

sand and surface residual balls 

(SRBs) along the Alabama and 

Florida Gulf coast, after Shields 

(1936) shown as a function 

of density and grain size for 

six particle sizes. For each 

standardized surface residual 

ball (SRB) grain size (table 1), 

we calculate the critical stress 

for the range of observed SRB 

densities, with the resultant 

critical stress mean and one 

standard deviation shown. 

The critical stress calculated 

for each size using the mean 

SRB density is within the 

small range of variability but is 

greater than the critical stress 

of a particle of the same size 

with the density of quartz sand.

Inlet Dynamics and Sediment Mobility

The influence of tidal currents on sediment transport, 

including sand and SRBs, in the vicinity of tidal inlets and 

estuaries is more complicated than the open-coast analysis 

where wave-generated alongshore currents dominate flow 

patterns. Inlet effects caused by tidal flows and their interaction with the incoming wave field (wave-current interaction) 

were evaluated across the model domain for 24 hours using 

wind and wave parameters of scenario H4_D7 (fig. 2). 

Identifying inlet convergence and divergence patterns 

requires detailed shallow bathymetry at the inlet. The model 
10 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

grid used for inlet simulations at Pensacola Pass, Fla., Little 

Lagoon, and Panama City (fig. 1) therefore included higher 

(for example, 1- to 50-m) alongshore resolution within the 

three inlets. The flow field and water levels were coupled with 

the wave model every 3 hours to include the effects of flow 

and water level processes on the incoming waves for simulations of sediment mobility at inlets.

Metrics for Evaluating Sand and SRB Mobility 

and Redistribution Patterns

Analyses were conducted to determine sediment and SRB 

movement probability and alongshore redistribution patterns 

for SRBs of size classes for each individual scenario, illustrating the likely mobility and redistribution patterns under 

the conditions that scenario represents. In addition, metrics 

of mobility and alongshore potential flux were calculated as 

weighted averages of all the scenarios, indicating probable 

patterns in mobility and redistribution over longer time scales, 

and mobility over a 24-hour period was calculated for one 

scenario to assess the variability in mobility over a tidal cycle.

Metrics for hydrodynamic and SRB and sediment movement probability and alongshore redistribution for wave 

scenarios are:

• significant wave height;

• maximum and median alongshore current;

• alongshore current convergences;

• alongshore current decelerations;

• mobility ratio; and, 

• potential flux.

Two additional metrics used to assess the overall probability of mobility and alongshore distribution over the time 

period of interest are:

• weighted mobility probability; and, 

• weighted potential flux.

The range of tidally induced SRB and sand mobility over

a 24-hour period for one scenario is evaluated with:

• tidal mobility.

These metrics are listed in table 2 with the naming 

convention of the associated output shapefiles (appendix 4). 

Metric calculations are described below.

Significant Wave Height

The significant wave height (metric 1) is calculated by 

the Wave module of Delft3D for each scenario. This parameter 

is an output of the model, is converted to Esri ArcGIS polygon shapefile format over the model domain, and is included 

to illustrate the spatial variability in wave height for each 

scenario.

Maximum and Median Alongshore Current

The alongshore component of the flow velocity within 

the surf zone was extracted from each scenario simulation (for 

example, see fig. 4). The modeled surf zone for each scenario 

was defined as stretching from the shoreline out to the crossshore location of maximum wave height found between the 

shoreline and the most offshore point of modeled, depthinduced wave breaking dissipation. The maximum and median 

surf zone alongshore current at each alongshore location, for 

each scenario, was extracted within this surf zone (metric 2). 

The currents (maximum and median) were smoothed over a 

2-km alongshore region to remove short-scale, noisy variations associated with grid-scale variations that were not well 

resolved.

Alongshore Current Convergences

The alongshore varying maximum velocity computed 

above was used to identify flow convergences (metric 3) and 

decelerations in the magnitude of flow in the direction of flow 

movement, indicating locations where the alongshore transport 

of SRBs would be disrupted and deposition would be more 

likely (fig. 10). Locations of convergences in the maximum 

Table 1. Classes of surface residual ball size and density considered in mobility, potential flux analysis, and critical stress in the 

northern Gulf of Mexico alongshore Alabama and Florida 

Class Size (cm) Density (kg/m3) Critical stress (Pa)

High Medium Low

Sand 0.03 2,650 0.20 na na

SRB1 0.03 2,107 0.15 0.06 0.03

SRB2 0.5 2,107 2.56 1.06 0.53

SRB3 1 2,107 5.80 2.12 1.06

SRB4 2.5 2,107 14.70 5.29 2.65

SRB5 5 2,107 29.26 10.58 5.29

SRB6 10 2,107 58.36 21.27 10.58
Methods 11

Table 2. Nine metrics for hydrodynamic and surface residual ball and sediment mobility and alongshore redistribution in the northern 

Gulf of Mexico along the Alabama and Florida coast.

[In the file naming convention for associated geographic information system shapefiles, Hh_Dd indicates the individual scenario bin number (fig. 2) and xxx 

indicates file type extension]

Metric # Name and description File naming convention

1 Significant wave height Hh_Dd_wave_height.xxx

2 Maximum and median alongshore current in the surf zone, spatially smoothed over 2 kilometers (km)Hh_Dd_current.xxx

3 Locations of alongshore current convergences* in the maximum alongshore current smoothed 

over 2 km

Hh_Dd_conv.xxx

4 Locations of alongshore current decelerations in the direction of flow (particles moving with 

the flow would encounter decreasing magnitude velocities) in the maximum alongshore 

current smoothed over 2 km

Hh_Dd_decel.xxx

5 Sand and SRB mobility ratio of the combined wave-current shear stress to the critical stress 

value for high, medium, and low critical stress values

Hh_Dd _mobility.xxx

6 SRB surf-zone integrated alongshore potential flux, smoothed over 2 km, for high, medium, 

and low critical stress values

Hh_Dd_potential_flux.xxx

7 Weighted mobility probability, for example, mobility for all scenarios weighted by probability 

of occurrence, for high, medium, and low critical stress

Weighted_mobility.xxx

8 Weighted potential flux, for example, surf-zone integrated alongshore potential flux, smoothed 

over 2 km, for all scenarios weighted by probability of occurrence

Weighted_potential_flux.xxx

9 Tidal mobility, for example, mobility ratio at each of 24 hourly time steps from a time-series 

simulation including tidal current and water level variation.

Tidal_mobility_TT.xxx

*

Not all scenarios have flow convergences. No convergence shapefiles exist for scenarios H3_D6, H4_D5, H4_D12, H4_D13, H5_D4, H5_D5, and H5_D12.

Figure 10. Two mechanisms of increased probability for surface 

residual ball (SRB) accumulation based on A, alongshore flow 

convergence and B, spatially decelerating flows.

alongshore current were computed by finding adjacent grid 

cells where the current velocity transitioned from eastwarddirected (positive alongshore velocity) to westward-directed 

(negative alongshore velocity). The convergence is always 

selected as the negative (westward) velocity cell.

Alongshore Current Decelerations

Spatial decelerations in the direction of flow (metric 4; 

for example, the flow velocity decreases from one grid cell to 

the adjacent cell in the direction of flow) were defined using 

an advective acceleration term, , where u is the alongshore 

current and y is the alongshore grid coordinate. The derivative 

of u was computed and used to identify locations where the 

flow decelerated ( less than (<) 0). We identified locations 

corresponding to peak deceleration (convex points in ) 

and the magnitude of u at the identified points was also 

recorded. Note that, for eastward flow (u greater than (>) 0), 

the u deceleration term is negative, whereas for westward 

flow (u < 0), the u deceleration term is positive. δu__

δy

δu__

δy

__δu

δy

δu__

δy

__δu

δy

__δu

δy
12 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Sand and SRB Mobility Ratio

Sand and SRB mobility (metric 5) was assessed by calculating the ratio of the spatially variant maximum combined 

wave-current bed shear stress (τWC) for each scenario (appendix 3) to the three critical stress values for each representative 

SRB class. A mobility ratio greater than one indicated critical 

stress value exceedance and, therefore, particle mobility. Also 

calculated was the mobility ratio of the local sand-sized sediment. When sand is mobilized, there is the potential for SRB 

exhumation or burial. The magnitude of the mobility does not 

indicate distance, direction, or velocity of transport. Movement may consist of rocking back and forth in wave action 

with no net motion or net cross-shore transport.

SRB Surf-Zone Integrated Alongshore Potential 

Flux

To assess alongshore transport patterns, the approach 

of Soulsby-van Rijn (Soulsby, 1997) was used to develop 

estimates of SRB combined suspended and bedload potential 

flux. The Soulsby-van Rijn method accounts for currents, 

which are the dominant force in alongshore transport, and 

waves, which contribute a stirring action that keeps particles 

in motion and allows them to move with current velocities 

otherwise too weak to support transport. The potential flux 

was calculated as the mass per second that would be transported across a meter span in the cross-shore. To estimate the 

total alongshore flux at each alongshore location, the potential 

flux (in kilograms per meter per second) in each grid cell was 

multiplied by the cross-shore width of that grid cell to attain 

the total rate of mass passing through the cell (in kilograms 

per second). Results from each grid cell in the surf zone at 

each alongshore location were then added together to attain 

the total potential rate of mass transfer (in kilograms per 

second), resulting in an integrated potential flux alongshore 

the surf-zone (metric 6). The alongshore variant potential flux 

for each scenario was smoothed with a sliding 2-km Hanning 

window (Bendat and Piersal, 1971) to remove smaller scale 

spatial variation not likely to be well resolved by the model.

The Soulsby-van Rijn formulation was developed to estimate flux for a uniform bed of particles of a given size. The 

actual flux in the case of a mixed bed, such as SRBs mixed in 

with sand, will be a function of the relative availability of each 

material. If no SRBs are present, then the flux for the materials 

in the bed will be 0. The spatial patterns in the potential flux, 

however, highlight areas where there are flux convergences 

and (or) zones of decreasing flux magnitude in the direction 

of flow, both of which would be more probable areas for SRB 

deposition. Conversely, flux divergences and (or) zones of 

increasing flux magnitude in the direction of flow are less 

likely to accumulate SRBs. The flux sensitivity to the three 

critical stress values described above (fig. 8) was considered 

in order to account for potential variability due to exposure 

above the sea floor.

Weighted Mobility Probability

In addition to individual scenario results, the results from 

multiple scenarios were combined to assess persistent patterns 

in mobility during April 1, 2010, to May 1, 2012. For each 

scenario, the mobility map was converted to a binary threshold 

map delineating locations where the critical value for mobility 

had been exceeded (value = 1) and not exceeded (value = 0). 

For sand and each SRB class and critical threshold value, an 

average of this threshold exceedance map was taken, weighted 

by the scenario probability of occurrence over the 2-year time 

period considered (appendix 1). The weighted mobility probability (metric 7) varies from 0 to 1, with values approaching 

1 indicating mobility under most wave conditions and values 

approaching 0 indicating little to no mobility under any wave 

conditions. The weighted mobility probability is a measure 

of the probability that SRBs or sand are mobilized and is 

analogous to the fraction of time at each location that mobility 

occurred over the time period of interest, whereas the mobility 

ratio for an individual scenario as previously described, which 

can be any number greater than or equal to 0, is the ratio of the 

stress to the critical threshold value for the single point in time 

represented by that scenario and must exceed 1 to indicate 

mobility under the conditions of the scenario.

Weighted Potential Flux

In addition to the potential flux for each individual 

scenario, an average surf-zone integrated potential alongshore 

flux (smoothed over 2 km in the alongshore direction) was calculated for each SRB class and critical stress threshold from 

all the scenarios, weighted by scenario probability (metric 8). 

This analysis shows patterns in SRB redistribution over all 

wave conditions during the 2-year period considered and may 

thus highlight persistent patterns in SRB alongshore redistribution, assuming that cross-shore processes did not transport 

SRBs and remove them from the surf zone (either through 

onshore deposition or loss to the shelf) between individual 

events.

Tidal Mobility

The tidal-inlet simulation produces a measure of tidally 

induced SRB and sand mobility near inlets, referred to as 

tidal mobility (metric 9). The simulation is based in part on 

metric 5 (table 2), the mobility ratio, and calculated hourly 

over a 24-hour tide cycle for scenario H4_D7. The results are 

output in polygon shapefile format for each of the 24-hour 

time steps. Appendix 5 includes the time step and shapfile 

(TT) corresponding to maximum flood and ebb for each inlet 

in the model domain, and file naming conventions are defined 

in appendix 4.
Results 13

Tidal Inlet Animations

In addition to tidal mobility metrics (table 2) assessed 

over the entire model domain for each size class of SRB 

and sand, animated movies (.avi file format) of the mobility 

of 2.5-cm SRBs and sand were created to demonstrate 

the temporal variation in mobility over the tidal cycle for 

Pensacola Pass, Fla., Little Lagoon, Ala., and Panama City, 

Fla. (fig. 1). See appendix 4 for file naming conventions.

Results

Model Evaluation

Wave Model

NDBC directional wave buoy, 42012, (National Data 

Buoy Center, 2012) off the coast near the Florida-Alabama 

border, is in 28-m water depth and lies within the OSAT3 

model domain (fig. 11). In addition, a wave-resolving acoustic doppler current profiler (ADCP) had been deployed in 

the project area. We used the observations from the ADCP to 

evaluate the accuracy of the wave model and to evaluate the 

suitability of the large-scale wave model to providing boundary conditions for the high-resolution model (K.T. Holland, 

Naval Research Laboratory, unpub. data, 2012). We evaluated 

the sensitivity of large-scale model predictions to changes 

in model resolution at the boundary using the Wavewatch 

III model results. The output of Wavewatch III 4′-resolution 

between May 2010 and May 2011 was compared with a validated, high-resolution ( 2′, or about 3.7 km) Simulating Waves 

Nearshore (SWAN; Booij and others, 1999; Ris and others, 

1999) wave hindcast that was run by the USGS Woods Hole 

Coastal and Marine Science Center and to data from NDBC 

buoys in the northern Gulf of Mexico (National Data Buoy 

Center, 2012; fig. 11) over the longer time period of May 2010 

to May 2012. Output from the closest grid cell to each buoy 

was used for model validation. Results from Wavewatch III 

and SWAN was comparable to data from three NDBC buoys 

(42012, 42039, and 42040). Specifically, at all three buoys the 

difference in bias (that is, mean) and root-mean-square (RMS) 

error in wave height (in meters) and period (in seconds) 

between the models was less than 0.2 m (fig. 12; table 3). The 

overall bias and RMS error, respectively, for the 2-year period 

were –0.10 m and 0.20 m for significant wave height and 

–0.56 s and 1.28 s for wave period at buoy 42012, the closest 

buoy to the project site. A similar magnitude of error was 

obtained at two more offshore northern Gulf of Mexico buoys 

(table 4). This analysis demonstrates that the Wavewatch 

III model resolves wave conditions sufficiently to provide 

boundary conditions for the OSAT3 domain, and that accuracy 

would not be improved by running a higher resolution model 

to provide boundary conditions.

Timeseries of simulated wave conditions were extracted 

from the 80 simulation scenarios by comparing the observed 

wave height and direction at buoy 42040 to the scenario 

definitions and selecting the best-fit scenario for each hour. 

Then, simulated wave conditions at each hour were compared 

to observations from buoy 42012 (fig. 13). This evaluation 

demonstrates the modeled wave transformation from the 

offshore boundary to the interior of the OSAT3 model domain. 

Wave height was predicted well at this location, whereas 

directions were predicted well for offshore waves propagating 

at a mean direction from the south, southeast, and southwest, 

Figure 11. NDBC directional 

wave buoys (42012, 42039, and 

42040) and a Naval Research 

Laboratory (NRL) acoustic 

doppler current profiler (ADCP) 

used for model evaluation 

along the Alabama and Florida 

Gulf coast. 
14 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Figure 12. Comparison of 

Wavewatch III and SWAN 

model output to significant 

wave height and wave period 

observations at NDBC buoy 

42012 between May 1, 2010, 

and May 1, 2011. 

Table 3. Comparison of high resolution SWAN model output to Wavewatch III model output, evaluated against observed buoy data 

from May 1, 2010, to May 1, 2011.

[m, meters; R2, coefficient of determination; RMSE, root mean square error; s, seconds]

Buoy Depth (m) Significant wave height (m) Peak wave period (s)

Bias RMSE R2 Bias RMSE R2

Wavewatch III

42012 27.7 –0.11 0.21 0.87 –0.58 1.33 0.49

42040 164.6 –0.02 0.22 0.88 –0.68 1.32 0.46

42039 307 –0.13 0.23 0.90 –0.68 1.24 0.48

SWAN

42012 27.7 0.00 0.21 0.81 –0.43 1.29 0.47

42040 164.6 0.00 0.21 0.88 –0.48 1.25 0.45

42039 307 –0.07 0.20 0.90 –0.53 1.21 0.47
Results 15

Table 4. Comparison of Wavewatch III model output to data from three northern Gulf of Mexico offshore NDBC buoys for the 2-year 

time period of from May 1, 2010, to May 1, 2012.

[m, meters; R2, coefficient of determination; RMSE, root mean square error; s, seconds]

Buoy Depth (m) Significant wave height (m) Peak wave period (s)

Bias RMSE R2 Bias RMSE R2

42012 27.7 –0.10 0.20 0.86 –0.56 1.28 0.49

42040 164.6 –0.02 0.21 0.90 –0.61 1.25 0.50

42039 307 –0.13 0.23 0.91 –0.72 1.29 0.46

Figure 13. Model predictions of A, wave height and B, wave direction from the 80 scenarios compared with observations at NDBC 

buoy 42012 in the northern Gulf of Mexico alongshore Alabama and Florida. Shown are scenarios when mean offshore wave direction 

(buoy 42040) was from the southeast, south, and southwest (wave direction bins D5–D12; fig. 2) and from northwest, north, and 

northeast (wave direction bins D1–D4 and D13–D16; fig. 2). The error statistics correspond to modeled waves for D5–D12 scenarios. 

but poorly for waves from the north. We note that northern 

waves observed at the offshore buoy (42040) and buoy 

42012 in about 30-m water depth usually correspond to small 

wave events along the coast of the northern Gulf of Mexico, 

which result in weak alongshore currents and therefore weak 

mobility or transport. These events also have a low probability 

of occurrence.

Finally, wave model predictions at Santa Rosa Island, 

Fla., for the winter time series (January 15–25, 2007) 

were compared with data collected by researchers at the 

Naval Research Laboratory (K.T. Holland, Naval Research 

Laboratory, unpub. data, 2012) for the same time period by an 

ADCP in approximately 12-m water depth. The comparison 

(fig. 14) shows that wave height was predicted within acceptable tolerance (0.24-m bias error and 0.31-m RMS error). 

Models of wave direction and periods produced a 27° and 

–1-s, respectively, bias error and 14° and 1-s RMS error, 

respectively. Largest errors in wave period and direction 

corresponded to the lowest wave heights (less than 0.5 m); 

these errors would have little impact on alongshore current 

or mobility calculation errors. The modeled peak period 

compares well with the observed mean period (fig. 14A–C).

Tide and Storm Simulations

NOAA operates tide stations at Dauphin Island, 

Pensacola Bay, and Panama City (National Oceanic and 

Atmospheric Administration, 2012). Observations from the 

permanent tide stations were used to evaluate the accuracy 

of water level predictions along the coast and into the bays 
16 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Figure 14. Model predictions of A, wave height (H), B, peak wave direction (Dp), and C, peak wave period (Tp) in the northern Gulf 

of Mexico alongshore Alabama and Florida for January 15–25, 2007, compared with observations (wavecis) from a Naval Research 

Laboratory acoustic doppler current profiler at Santa Rosa Island, Florida. To demonstrate the accuracy of the model, we show the 

values from NDBC buoy 42040 offshore in the northern Gulf of Mexico as an alternative model for predicting nearshore values. Only 

cases where the measured nearshore wave height exceeded 0.5 meter are shown.

within the project site for time-series simulations. We evaluated the accuracy of the tidal model using data from the tide 

stations for the January 15–25, 2007, time-series simulation. 

The comparison indicates minimal errors in both phase and 

amplitude at all locations (fig. 15).

The approach and landfall of Hurricane Isaac in late 

August 2012 was used to evaluate simulation accuracy under 

more extreme weather conditions. Wave characteristics and 

water level predictions were compared with waves measured 

at buoy 42012 (National Data Bouy Center, 2012) and to water 

level at the three NOAA tidal stations (National Oceanic and 

Atmospheric Administration, 2012; fig. 15). Wave height 

during the peak of the storm was slightly underpredicted, 

but predictions for mean wave direction and period showed 

reasonable approximations (fig. 16). It is not unusual for 

wind models to incorrectly predict the intensity of tropical 

storms (Rogers and others, 2006) and therefore lead to errors 

in modeled wave heights. The water level predictions underestimated water level observations at all locations (fig. 17). 

Our simulations relied on the large-scale models for adequate 

boundary conditions. We experimented with several different 

large-scale models to supply water level boundary conditions 

for the OSAT3 domain and determined that none of the 

alternate models offered improved accuracy compared with 

the others. The results here use HYCOM for large-scale water 

level boundary conditions at the OSAT3 model boundaries. 

Errors between the model and observations may reflect errors 

in the large-scale model predictions that provided boundary 

conditions to our simulations or shortcomings in the model 

implementation. The predictions were substantially improved 

compared with a simple astronomical prediction and captured 

Figure 15. Evaluation of accuracy of simulated (modeled) water 

levels (in meters) against NOAA tidal measurements at A, three 

coastal inlet tide stations at B, Dauphin Island, Ala., C, Pensacola 

Pass, Fla., and D, Panama City Inlet, Fla. Astronomical water 

level predictions are also shown. The model predictions include 

some noise in the initial spinup of the flow simulations, which 

disappears after a few tidal cycles. 
Results 17

the relevant dynamics associated with Hurricane Isaac’s 

approach and landfall to the west of the area of interest.

Scenario Simulation Results

Results of the modeling simulations were exported 

from the irregular model grid as point and polygon shapefiles 

and are available in the digital release of this report. Alongshore patterns in currents, mobility, and potential flux varied 

significantly among the 80 scenarios, depending on the wave 

height and angle of approach and the amount of alongshore 

variability in the incoming wave field; variability in mobility 

around the inlets was noted over a tidal cycle.

Scenario Analysis

Figures 18 through 21 illustrate hydrodynamic analyses 

(table 2, metrics 1 to 4) from two scenarios, H3_D6 and 

H3_D8 (fig. 2). The selected scenarios present an offshore 

wave height of 1 to 1.5 m but from slightly different wind 

directions, southeast and south-southeast, respectively. 

Significant wave height (metric 1) barely reaches 0.75 m 

near the coast with the southeast winds (scenario H3_D6; 

fig. 18A), but significant wave height exceeds 1m with the 

south-southeast winds (H3_D8; fig. 18B). Maximum alongshore velocity (metric 2) is westward under scenario H3_D6 

(fig. 19A) and mixed east and west under scenario H3_D8 

(fig. 19B). Flow convergence (metric 3; meters per second, 

m/s) is absent under scenario H3_D6 (fig. 20A) but occurs at 

several different locations in scenario H3_D8 with the southsoutheast wind (fig. 20B). Flow deceleration (metric 4; meters 

per second squared, m/s2) of varying magnitude and direction 

occurred under both scenarios (fig. 21). For scenario H3_D8 

(figs. 20B and 21B), a combination of south-southeast waves, 

offshore features, and orientation of the coast produced numerous flow decelerations and reversals. Under scenario H3_D6 

(figs. 20A and 21A), numerous alongshore convergences and 

spatial decelerations can affect the potential accumulation, 

burial, and removal of SRBs. The scenarios, while similar in 

originating wave energy and only 40° different in offshore 

wave angle, indicate that the movement of SRBs caused by 

alongshore flows is dependent on the specific wave conditions 

(for example, a specific time period of interest) and, potentially, the sequence of wave conditions over time that may 

allow SRBs to be transported from one area of accumulation 

to another.

The potential for movement of SRBs was assessed by calculating the mobility as represented by the ratio (table 2, metric 5) of the τWC for each scenario to the critical stress of incipient motion for each representative SRB class, with a mobility 

greater than 1 indicating that the threshold for mobility was 

exceeded (SRB and sand mobility section). For the H3_D6 

scenario shown in figure 22A, with offshore waves between 

1 and 1.5 m, the mobility threshold of 2.5-cm SRBs is only 

exceeded at isolated patches in the surf zone. In contrast, when 

Figure 16. Simulated and measured wave characteristics at 

buoy 42012 (fig. 11) in the northern Gulf of Mexico alongshore 

Alabama and Florida during Hurricane Isaac in August 2012. 

Characteristics include A, significant wave height, B, mean wave 

direction, and C, mean wave period. 

Figure 17. Simulation of water levels (in meters) in the northern 

Gulf of Mexico alongshore Alabama and Florida during Hurricane 

Isaac in August 2012 compared with measured water level at the 

NOAA tide stations at A, Dauphin Island, Ala., B, Pensacola, Fla., 

and C, Panama City, Fla. tide stations (fig. 15A) and to astronomical 

tide predictions.
18 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Figure 18. Significant wave 

height (table 2, metric 1) for 

scenarios A, H3_D6 and B, H3_

D8 (fig. 2) in the northern Gulf 

of Mexico alongshore Alabama 

and Florida. Nearshore wave 

height in each scenario 

originated with 1- to 1.5-meter 

(m)-high waves at National 

Oceanic and Atmospheric 

Administration buoy 42040, but 

with southeasterly and southsoutheasterly wind directions, 

respectively.

Figure 19. Maximum 

alongshore velocity (table 2, 

metric 2) smoothed over a 

2-kilometer length scale for 

scenarios A, H3_D6 and B, H3_

D8 (fig. 2) in the northern Gulf 

of Mexico alongshore Alabama 

and Florida. Green and red 

arrows indicate eastward- and 

westward-directed flows, 

respectively. Flow is to the 

west throughout the domain 

in A, whereas there are mixed 

flow directions in B. 
Results 19

Figure 20. Flow convergence 

(table 2, metric 3) for scenarios 

A, H3_D6 and B, H3_D8 (fig. 2) 

in the northern Gulf of Mexico 

alongshore Alabama and 

Florida. Flow reversals are 

absent in A, whereas several 

flow reversals were identified 

in B and correspond to color 

changes in fig. 19B.

Figure 21. Flow deceleration 

(table 2, metric 4; as change, 

delta, d, meters per second 

squared, m/s2

) for scenarios 

A, H3_D6 and B, H3_D8 (fig. 2) 

in the northern Gulf of Mexico 

alongshore Alabama and 

Florida. Spatial decelerations 

of varying magnitudes are 

found in both scenarios.
20 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Fiugre 22. Mobility ratio (table 

2, metric 5) in the northern Gulf of 

Mexico alongshore Alabama and 

Florida for a midlevel threshold of 

2.5-centimeter surface residual 

balls (SRBs; table 1) for scenarios 

A, H3_D6 and B, H4_D6 (fig. 2). Areas 

with a mobility ratio of 1 (in pink) 

indicate where the mobility threshold 

was exceeded. Whereas the mobility 

threshold is exceeded only in small 

sections in very shallow water in 

A, the large wave heights result in 

mobility along the coast as well as 

over shallow bar and ebb tidal delta 

features in B.

Figure 23. Mobility ratio (table 2, 

metric 5) in the northern Gulf of 

Mexico alongshore Alabama and 

Florida for sand for scenarios 

A, H3_D6 and B, H4_D6 (fig. 2). 

Areas with a mobility ratio of 1 (in 

pink) indicate where the mobility 

threshold was exceeded. Compared 

with 2.5-centimeter surface residual 

balls (SRBs; fig. 22), sand is mobile 

over a large portion of the domain in 

both scenarios, yielding the potential 

for exhumation and burial of SRBs in 

regions where the SRBs themselves 

are immobile.
Results 21

the waves come from the same direction but the wave height 

increases to between 1.5 and 2 m, the mobility threshold of 

2.5-cm SRBs is exceeded in a narrow band along the coastline 

and over shallow bar features (fig. 22B). In comparison, sand 

is mobilized under a significantly larger portion of the domain 

for both scenarios (fig. 23), with an associated potential for 

SRB exhumation or burial. In the case of northerly wind and 

wave scenarios (H5_D1), significant mobility may be found in 

some locations along the bay side of barrier islands (fig. 24).

The surf-zone integrated potential alongshore SRB 

flux (smoothed over 2 km) for each scenario and SRB class 

was calculated as described in the Methods section (table 2, 

metric 6; kilograms per second, kg/s). High, medium, and low 

critical stress estimates were analyzed to quantify the uncertainty in the potential flux estimates due to SRB exposure 

above the sea floor. Values less than 0 indicate transport to 

the west, values greater than 0 indicate transport to the east, 

values equal to 0 indicate no potential transport. Because of 

the limited mobility in scenario H3_D6 (fig. 25A), the potential flux is virtually 0, whereas for H4_D6 (fig. 25B), there 

are areas of potential flux (table 2, metric 6) throughout the 

domain for the model. The potential flux may be used to estimate likely spatial patterns in SRB redistribution; for example, 

in the illustrated scenario, 2.5-cm SRBs are more likely to be 

deposited where the magnitude of the westward potential flux 

decreases (fig. 25B detail).

Figure 24. Mobility ratio (table 

2, metric 5) in the northern Gulf of 

Mexico alongshore Alabama and 

Florida for a midlevel threshold of 

2.5-centimeter (cm) surface residual 

balls (SRBs; table 1) along the Gulf 

Islands National Seashore (east of 

Pensacola Pass, Florida) for wave 

scenario H5_D1, corresponding to 

waves observed at NDBC buoy 42040 

of height greater than 2 meters and 

coming from a north-northeasterly 

direction (fig. 2). Where the mobility 

ratio exceeded 1 (in pink) mobility 

of 2.5-cm SRBs was indicated at 

locations along the back-barrier 

from northerly wind-waves locally 

generated behind the barrier.

SRB and Sand Weighted Mobility Probability and 

Potential Flux

The weighted mobility probability for SRB class 4 

(fig. 26), calculated as described in Methods (table 2, 

metric 7), varied from 0 to 1, with values approaching 

1 indicating that the mobility threshold was likely to be 

exceeded under most wave conditions, and values approaching 

0 indicating mobility was unlikely under most conditions. 

Weighted mobility, which is the probability of mobility 

threshold exceedance, is analogous to the fraction of time 

an SRB of this size class is mobile. The variability between 

high, medium, and low mobility estimates provide a measure 

of the uncertainty in SRB mobility due to uncertainty in the 

estimation of critical stress thresholds. Alongshore Alabama 

and Florida on the northern Gulf of Mexico, 2.5-cm SRBs that 

are flush to the bed (highest estimate of critical stress among 

samples analysed; fig. 26A) are rarely mobilized, whereas 

SRBs more exposed to the flow field (lowest estimate of 

critical stress; fig. 26B) have a probability of mobilization of 

0.6, corresponding to mobility approximately 60 percent of the 

time.

The weighted surf-zone integrated potential flux (table 2, 

metric 8; kg/s) is a measure of the long-term patterns in probable SRB movement. There is a convergence in the weighted 

potential flux of 2.5-cm SRBs around Pensacola Pass, indicating SRBs of this size are likely to accumulate at this location 

(fig. 27).

Tidal-Inlet Time-Series Results

The analysis of SRB and sediment mobility over a 

24-hour period illustrates variability as a result of the tidal 

cycle. The variation in SRB mobility that can occur between 

ebb and flood near a coastal inlet can potentially lead to 

increased probability of SRB deposition within the lagoon 

over the tidal cycle (table 2, metric 9; fig. 28). The variation 

over the tidal cycle in mobility of sand and 2.5-cm SRBs can 

also be observed in animations, which are included in the 

digital release of this report, for the inlets at Pensacola Pass, 

Little Lagoon, and Panama City.
22 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Figure 25. Surf-zone integrated 

alongshore potential flux smoothed 

over 2 kilometers (table 2, metric 6) for 

2.5-centimeter surface residual balls 

(SRBs; table 1) in the northern Gulf of 

Mexico alongshore Alabama and Florida for 

scenarios A, H3_D6 and B, H4_D6. Because 

of the limited mobility in A (fig. 23), there is 

virtually no potential flux, whereas there 

is westward potential flux throughout the 

domain in B. Areas where the magnitude of 

the flow decreases (B, inset) are more likely 

areas of SRB deposition. 

Figurre 26. Weighted mobility probability 

(table 2, metric 7) from April 2010 to May 

2012 along the Gulf Islands National 

Seashore (east of Pensacola Pass, Fla.) 

for 2.5-centimeter surface residual balls 

(SRBs). Shown is an estimate using 

A, the highest estimate of critical stress, 

appropriate for SRBs flush with the seabed, 

and B, the lowest estimate of critical 

stress, appropriate for SRBs sitting atop the 

seabed. 
Results 23

Figure 27. Weighted surf-zone 

integrated alongshore potential flux 

(table 2, metric 8), indicating the 

average potential flux in the northern 

Gulf of Mexico alongshore Alabama 

and Florida from April 2010 to May 

2012 for 2.5-centimeter surface 

residual balls (SRBs; table 1) using 

a midrange estimate of critical 

stress. There is a convergence in the 

probable flux at Pensacola Pass, Fla., 

and divergence toward the east of 

Pensacola Pass.

Figure 28. Tidal inlet surface 

residual ball (SRB) mobility (table 2, 

metric 9) at A, maximum flood and 

B, maximum ebb for 2.5-centimeter 

SRBs (table 1) using a low critical 

threshold at Little Lagoon Inlet, Ala. 

(fig. 1). Areas where the mobility 

ratio is 1 (in pink) indicate that the 

critical threshold for SRB mobility 

is exceeded. The greater extent of 

tidal inlet SRB mobility during flood 

increases the probability that SRBs 

brought in by the tide will remain 

trapped. Local surficial sediment is 

mobilized throughout the illustrated 

domain during both flood and ebb 

tide, leading to potential for burial and 

exposure of SRBs.
24 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Discussion

Implications of Results for Understanding SRB

Formation, Burial, Exhumation, and Transport

The results of the numerical modeling allow specific conclusions to be drawn for a given time period of interest based 

on the scenario or on scenario-averaged results that indicate 

patterns in alongshore currents and their gradients, sediment 

and SRB mobility and potential transport, gradients, and complexities associated with tidal inlets under specific conditions. 

The results can be used to address many detailed questions; in 

this section, we identify and discuss some general findings that 

directly address the objectives of the OSAT3 subgroup.

Alongshore-Currents and Gradients in Transport

A primary objective of the OSAT3 subgroup effort was 

to identify regions of varying alongshore current speeds and 

directions, resulting in areas of persistent convergence and 

divergence of alongshore currents and, by inference, the 

deposition of SRBs. A striking example of convergence was 

detected in the model at Pensacola Pass where, because of the 

bend in the shoreline, alongshore flows and therefore potential 

SRB flux were directed toward the inlet (fig. 29). In this situation, SRBs occurring nearshore would be transported toward 

the inlet. This situation could lead to an increase in the complexity of SRB transport because waves, alongshore flows, and 

tidal currents would all interact with the sediment and SRBs.

Figure 29. A, Maximum alongshore 

flow speed (green and red arrows) 

smoothed over a 2-kilometer 

length scale (table 2, metric 2) and 

B, mobility ratio (table 2, metric 

5) using the lowest critical stress 

threshold, appropriate for surface 

residual balls (SRBs) sitting on top 

of the seabed, for 10-centimeter 

SRBs (table 1) near Pensacola Pass, 

Fla., for scenario H5_D8 (fig. 2). All 

small-size classes of SRBs are also 

mobilized, leading to convergence 

and a high probability of deposition 

in Pensacola Pass during the wave 

conditions represented by this 

scenario.

Inlet Dynamics

Inlet dynamics are complicated because they respond 

strongly to tidal- and storm surge-driven currents that affect 

both the inlet interior and open coast. These flows interact 

with a variety of morphological features including the sand 

spits at the inlet, ebb and flood delta shoals, sandbars and sand 

flats inside the inlet, and surf zone bars extending along the 

inlet spits (fig. 30). The interaction of morphology and tidal 

flow typically produces asymmetries in flow patterns that 

consist of strong flood tides in the channel, strong currents 

along the shoreline entering the inlet, and ebb flow jets that are 
Discussion 25

Figure 30. A, Morphologic 

features (yellow arrows) at 

the Pensacola Inlet, Fla., that 

interact with the tidal flow (pink 

arrows—solid arrows indicate 

flood tide flows and dashed 

arrows indicate ebb tide 

flows). B, Modeled inlet flow 

speeds and C, 2.5-centimeter 

surface residual ball (SRB) 

mobility for low threshold 

calculations during flood tide 

with moderately large waves 

(scenario H4_D7; fig. 2). Areas 

where the mobility ratio is 1 (in 

pink) indicate that SRB mobility 

threshold is exceeded.

focused by the channel. Hence, there can be a net tidal inflow 

along the shoreline. If SRBs exist along that shoreline, they 

can, therefore, be directed toward and concentrate in the inlet. 

Additionally, inlets may be wide enough to allow waves to 

enter the estuary and support mat and SRB deposition on sand 

flats, multiple sandbars, and shorelines in the presence of oil.

Complexity of Coupled SRB and Sand Dynamics

The complexity of the SRB source, burial, exhumation, 

and transport of SRBs relevant to the OSAT3 objective to 

define or determine reoiling mechanisms is explained in the 

predicted variation in the timing and spatial extent of SRB 

and sediment mobility. The simulations demonstrate that, 

compared with sand, SRBs are less likely to be mobilized by 

any specific set of conditions (figs. 9 and 31) and therefore are 

often at the mercy of sediment deposition or erosion. Because 

larger SRBs are less likely to move than smaller SRBs, it is 

possible that transport processes will segregate the different 

sizes of SRBs. For instance, lag deposits of large SRBs may 

be created and subsequently buried or exhumed by the movement of local sediment.

Effect of Assumptions

Scenario Selection

We assume that a broad range of actual conditions was 

well represented by the subset of conditions defined by our 

wave height-direction scenarios. To test this assumption, we 

used the results from the 80 scenarios to reconstruct a simulated wave time series to compare to observations collected 

from the Naval Research Laboratory ADCP off the coast at 

Santa Rosa Island in 12-m water depth. The reconstruction 

is calculated using the observed time series at the offshore 

NDBC buoy 42040 and, for each hour, assigning each scenario 

with the likelihood that it best represents this time period 

based on observed wave height, direction, period, and wind 

speed and direction. The modeled wave parameters at the 

nearshore location for each scenario are multiplied by the 

respective likelihood values and summed across all scenarios. 

If our set of scenarios represents the range of conditions that 

exists over this region, then the waves reconstructed from the 

scenarios should compare well with the nearshore observations. The bias and RMS error in wave height for this reconstruction were 0 m and 0.26 m, respectively (fig. 32), which 

is as accurate as the time series comparison (compare with 

fig. 14).

SRB Size, Shape, and Exposure

The calculations forming the basis of shear stress estimation, mobility, and potential flux parameters used in this 

analysis have been most extensively validated in the nearshore 

environment for sand-sized particles by Soulsby (1997) and 

Soulsby and Whitehouse (1997). Application and validation 

of formulations for these processes for cobble or mixed sand 

and cobble beaches in a similar size range to SRBs have been 

limited (Van Wellen and others, 2000; Boyer and others, 2002; 
26 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Soulsby and Damgaard, 2005), and there has been no known 

previous application specifically to SRBs. The extension to 

very large particles, such as SRBs, that may not be spherical 

and are sparsely distributed on the sand matrix of the seabed 

requires consideration of the influence of shape and exposure 

of the SRBs. The findings from the existing literature on 

mixed grain sizes and shapes were used to constrain the range 

of critical shear stresses required to mobilize SRBs (fig. 8). 

Exposed SRBs would be more likely to move than SRBs that 

are hidden through burial. Shape was considered less important since flat objects would have reduced exposure compared 

with round objects, even though their transport might be 

enhanced once they were tipped up on edge and mobilized. 

It is not known how an aggregate of sand and oil, such as an 

SRB, would behave differently than a solid object, such as a 

cobble, as a result of deformation, disintegration, or interaction with the surrounding sediment.

Figure 31. Mobility 

ratios (table 2, metric 5) of 

A, 0.03-centimeter (cm) quartz 

sand (sediment); and B, 2.5-

cm and C, 10-cm surface 

residual balls (SRBs) under 

large wave (more than 2-meter) 

conditions in the northern Gulf 

of Mexico alongshore Alabama 

and Florida corresponding 

to scenario H5_D8 (fig. 2). 

Where the mobility ratio is 1 

(pink areas), the SRB mobility 

threshold is exceeded. 

Sediment is more mobile 

than centimeter-sized SRBs, 

with mobility decreasing with 

increasing SRB size.

Figure 32. Observed wave height at the Naval Research 

Labortory acoustic dopler current profiler (ADCP) in the northern 

Gulf of Mexico alongshore Alabama and Florida for September 15, 

2006, through December 23, 2007, against the reconstructed wave 

height using corresponding subset of modeled scenarios.

Focus on Alongshore Processes

The analysis in this report did not explicitly account for 

cross-shore transport processes but rather focused on predicting the potential for alongshore movement of SRBs. Although 

the influence of oscillating currents beneath waves and tidally 

driven flows at inlets is included in mobility estimates, the 

cross-shore transport caused by these processes was not considered, and cross-shore currents such as rip currents were not 

considered in either mobility or potential flux calculations. The 

numerical model also did not account for hydrodynamic processes in the extremely shallow swash zone, which may result 
Discussion 27

in cross-shore or alongshore transport of SRB-sized objects 

(Osborne, 2005). Based on the observational data, SRBs must 

be transported in the cross-shore direction, particularly near 

the shoreline where SRBs are often recovered. Based on their 

large size, it is likely that SRBs are dominated by bed load 

transport mechanisms, which is driven onshore under asymmetric flows beneath breaking or almost breaking waves 

(Bowen, 1980). In simplified terms, the onshore-directed flow 

beneath wave crests is higher in magnitude but occurs for a 

shorter time than the offshore-directed flow beneath wave 

troughs. Because bed load transport responds to the flow speed 

raised to some power (typically assumed to be cubed) of the 

velocity, the net average transport is in the onshore direction. 

However, these simple formulations have not produced 

accurate predictions of cross-shore sediment movement and 

it is not clear at present how to solve the coupled sand-SRB 

transport problem.

Hence, our focus on the alongshore transport aimed at 

answering the questions “Are SRBs of a given size mobilized 

under a specific set of conditions?” and “If SRBs move, then 

what is the probable distribution pattern caused by alongshore 

processes?”. Implicit in this approach was an assumption 

that cross-shore processes would not actually contribute to 

modulating the alongshore transport, such as by concentrating 

SRBs in a cross-shore location of relatively high or relatively 

low alongshore current speeds or by preferentially transporting SRBs either landward onto shore or seaward onto the shelf 

and out of the surf zone domain.

Static Bathymetry

For the most part, the bathymetry used to support the 

numerical modeling did not vary in time. The NGDC dataset resolved features that were 30 m or larger and included 

nearshore sandbars and shoreline with substantial spatial 

variability. However, this variability was aliased by our 

relatively coarse alongshore resolution of about 250 m. This 

resulted in some apparent short-scale variations in alongshore 

currents and mobility that likely did not accurately reflect true 

variations at the 250-m scale. This short-scale variability was 

addressed though alongshore smoothing over a 2-km-length 

scale of the alongshore currents and potential flux, although 

mobility estimates were not smoothed. At Little Lagoon 

Inlet, Ala., high resolution data were required to resolve the 

inlet, and the model domain’s alongshore resolution was 

increased to about 1 m. This increase in resolution improved 

the detail and fidelity of the inlet dynamics at this location. 

However, compared with the uncertainty introduced by the 

critical threshold (for example, the dependency of mobility 

on SRB exposure, quantified by the difference between the 

high, medium, and low mobility estimates), small bathymetric 

changes are expected to have a relatively minor impact on 

mobility calculations. The details of the inlet and its surrounding shoal and channel features, however, can change substantially with time through natural processes as well as dredging. 

We note that comparing simulations that incorporated updated 

bathmetric elevations around Little Lagoon Inlet with those 

that did not incorporate updated bathymetric elevations, 

showed a change in maximum alongshore currently velocity of only about 10 centimeters per second. While the exact 

shape of the alongshore profile can be drastically affected 

by small changes in the bathymetry, the statistics we use to 

compute quantities, such as potential flux, do not appear to 

be impacted. Changes in mobility will depend on the magnitude of the change in bathymetry. A large change in depth 

can significantly affect mobility. Change in mobility will also 

depend on how close the original stress was to the threshold 

value. If the original stress was well over the threshold, it will 

likely continue to exceed the threshold and vice versa. A variety of indirect effects potentially exist that may be important 

to mobility and flux and are too numerous to evaluate here, 

such as changes in bathymetry offshore leading to changes in 

wave dissipation, wave height, and currents.

Accuracy of Boundary Conditions

For the boundary conditions for our model, we identified specific times when the Wavewatch III hindcast data 

matched the conditions of each scenario and thus assumed that 

the hindcast data on the high-resolution boundary accurately 

reflected conditions for the scenario. No attempt was made 

to correct these boundary conditions with buoy data. Instead, 

the buoy data on the interior of the high-resolution domain 

were used to evaluate the accuracy of our approach. In the 

case of the two time series (data from Santa Rosa Island, Fla., 

in 2007 and during Hurricane Isaac in August 2012), we also 

assumed that the model inputs of tides and storm surge were 

accurate. Errors in water levels, particularly during Hurricane 

Isaac (for example, fig. 15) may be due to boundary conditions errors, bathymetric errors, or other errors associated 

with model implementation and simplification. Based on the 

model-data comparisons that we have analyzed, we concluded 

that the predictions are skillful and, in spite of some errors, 

provide estimates of oceanographic variables that are significant improvements compared with climatologic or astronomic 

predictions.

Research Gaps

The numerical modeling of SRB behavior and the 

application of the model results to the OSAT3 objectives have 

identified several fundamental knowledge gaps relevant to our 

understanding of the formation, movement, evolution, burial, 

and exhumation of SRBs. Some of these knowledge gaps 

require additional, focused research, and other gaps require 

enhanced observations to support research and operational 

OSAT3 objectives. For example, at the outset of the numerical 

modeling planning effort, we recognized the lack of the ability 

to predict the details of cross-shore sediment and SRB transport responsible for changing the position of the shoreline, 

offshore sandbars, and SRBs. The shoreline reoiling problem 
28 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

required better understanding and prediction of these processes to better understand if and when SRBs in the surf zone 

will be transported and deposited on the shoreline or beach. 

To achieve the OSAT3 objectives, the cross-shore distribution 

of alongshore transport was addressed and resolved by the 

numerical model. Utilizing this knowledge for further practical 

applications of the results requires specifying the cross-shore 

distribution of SRBs. This gap was filled through nonmodeling 

techniques developed by other researchers in OSAT3, which 

included observations from cleanup and SRB recovery efforts, 

measurements of cross-shore profiles, and vertical and stereoimage analysis.

The broader OSAT3 analysis and discussion (which 

included observations of morphologic change and collections 

of SRBs on the beach and in the surf zone that was not 

described in this report) considered the spatially variant probability of mat formation, but did not include hydrodynamic 

variability such as variations in waves and water levels that 

were the subject of the current modeling effort. In addition, the details of the formation of SRBs from mats were 

not considered. Thus, SRB behavior assessments relied on 

extrapolation from studies not necessarily focused on agglomerates of sand and tar. Specific, detailed studies of SRBs on 

which to demonstrate good understanding and predictive skill 

were lacking during the course of this analysis.

Future Research Opportunities

Gaps in prediction capability and fundamental understanding of SRB behavior could be filled by additional effort 

on the following topics.

Research on modeling of cross-shore sediment transport 

processes to accurately predict shoreline and sandbar 

changes.—Currently [2012], only parameterized modeling 

approaches (for example, Plant and others, 1999; Yates 

and others, 2009, 2011) appear to have skill in applications 

to accurately simulate shoreline and sandbar changes, but 

these simplified approaches require persistent time-series of 

observations for calibration. Fundamental understanding of 

cross-shore sediment transport would likely provide better 

simulations of waves, water levels, and currents. This research 

pursuit has been ongoing for more than 30 years (Stive, 1987).

Research on mat and SRB formation.—The environmental conditions that were conducive to mat and SRB formation were identified by the overall OSAT3 effort, whose scope 

included collection of field observations of SRB occurrence. 

These included open-coast shorelines and, typically, shallow 

sandbars that were likely exposed or nearly exposed at low 

tide. Additionally, mat and SRBs were observed near and 

inside inlets where tidal and wave action likely contributed to 

their distribution. However, observations demonstrate substantial variability in the location of mats and resulting SRBs. 

Studies that investigate the details of mat formation, variability with changing hydrodynamic conditions such as tidal 

or surf water level or wave conditions, and response to burial 

and exhumation and creation of SRBs would further improve 

understanding of SRB behavior.

Research on observed SRB movement, burial, 

exhumation, and alteration.—The simulations of SRB 

mobility include many uncertainties associated with SRB 

shape and interaction with sand-sized sediments that affect 

SRB exposure to the mobilizing and transporting flows. No 

direct observations of particle movement of comparably sized 

and dense SRBs were available to test the model predictions, 

nor do fundamental data, such as friction coefficients between 

SRBs and the sea floor, exist to allow development of singleparticle tracking analysis to estimate distance traveled and 

velocity. Very little is known about the breakup of mats 

into SRB particles and of large, angular SRBs into smaller, 

rounded SRBs. Observations of SRB surrogates in laboratory 

and field settings could provide improved predictions for 

future applications to responses for reoiling or similar contaminants.

Operational Applications of Results and Methods

The modeling effort and the interaction of the subteam 

with the overall OSAT3 yielded a number of potential capabilities that could support the ongoing response to beach 

reoiling and provide guidance for future response activities 

associated with oil spills or other beach contamination situations. Here, we list several operational activities that could 

be implemented with or without further effort on the research 

gaps listed above.

Operational hindcast, nowcast, and forecast of SRB 

movement.—The methods employed under OSAT3 to simulate 

SRB movement are capable of providing substantially more 

detail into past, ongoing, and future reoiling. The operational 

challenges that can be overcome include developing a methodology to reconstruct detailed time series from a small number 

of scenarios, formal integration of oiling and SRB observation 

histories with simulated time series, and providing forecasts 

and uncertainties to be used in prioritization of cleanup 

response efforts.

Operational observations of shoreline and sandbar 

changes.—Observations of actual bathymetry and topography 

to resolve shoreline and sandbars and the nearshore seabed 

were valuable to understanding the likely locations of mats 

and SRBs and to simulation of waves and currents that drive 

SRB movement. The value of aerial imagery for shoreline and 

sandbar position and elevation estimates demonstrated that a 

range of ground-truth and remote sensing methods could be 

applied to this or similar responses. There is an opportunity to 

couple observation tasking with oceanographic models to optimize data acquisition. Formal evaluation of what data should 

be collected at what frequency and at what locations could be 

conducted with the present approach.

Operational assessment of the time-varying water-level 

intersection with intertidal bars and beach.—The OSAT3 

identified that SRB source mats formed near the shoreline. 

However, the shoreline varies with tide and wave conditions, 
References Cited 29

both of which vary in time. An alongshore variant time 

series of water excursion probability during oiling could be 

developed from existing extensions to the present modeling 

approach and be used to identify a two-dimensional probability distribution of mat formation locations. This analysis 

could include wave runup and swash elevations. In addition, 

variability in bathymetry around inlets and ebb or flood tidal 

deltas or over very shallow sandbar features could be assessed 

to further quantify the uncertainty in potential buried mats at 

these locations.

Summary And Conclusions

U.S. Geological Survey scientists have developed a 

model-based assessment of transport and deposition of residual oil that is causing shoreline reoiling within the northern 

Gulf of Mexico in the form of mixtures of sand and weathered 

oil, known as surface residual balls (SRBs). The results of 

the assessment can be used to provide guidance for ongoing 

response activities and data collection needs as well as to 

guide response for future oil spills or related events.

Results from these modeling efforts have identified spatial and temporal variations in alongshore currents, including 

locations where there are gradients resulting in convergences 

and decelerations in the flow. Likewise, the results identify 

spatial and temporal variations in the mobility of sand and 

SRBs. A striking example of convergence identified by the 

model was shown at Pensacola Pass, Fla., where trends in the 

orientation of the adjacent shoreline cause flow and potential 

SRB flux to be driven toward the inlet. This situation forces 

SRBs to interact with tidal currents, and the complexity of the 

situation is exacerbated by SRBs interacting with sandbars and 

channels which are themselves undergoing constant reconfiguration as wave and tide conditions change.

Modeling results suggest that, under the most commonly 

observed low-energy wave conditions, larger SRBs are not 

likely to move very far alongshore. This finding suggests that, 

under nonstorm condtions, large SRBs from one source location may not be redistributed to other alongshore locations. 

Under storm conditions, however, it is possible for larger 

SRBs to be mobilized. SRBs are likely to become buried and 

unburied under normal sand transport processes because they 

are less mobile than sand, thereby lengthening the time SRBs 

take to move onshore and adding a layer of complexity to the 

model.

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Appendix 1. Scenarios 33

Appendix 1. Scenarios

In this appendix, we define scenarios for reducing the full-time series to representative conditions and identify time periods 

that represent these scenarios for running simulations with spatially varying boundary conditions. As described in the Methods 

section of this report, scenarios were defined by drawing observations from 5 wave height ranges (i.e., bins) and 16 wave direction ranges, yielding 80 unique scenarios. The specifications for each scenario are defined in table 1–1. In addition to being 

defined by wave height and direction, the scenarios are further described by the conditional mean values of wave period, wind 

speed, and wind direction based on the observed data (from NDBC buoy 42040) for each scenario (fig. 1–1).

Table 1–1. Wave height and direction scenarios.

[m, meters; °, degrees; >, greater than]

Scenario Wave height bin, in m Wave direction bin,1 in ° Percentage of 

observations Representative date and time

H1_D1

H1_D2

H1_D3

H1_D4

H1_D5

H1_D6

H1_D7

H1_D8

H1_D9

H1_D10

H1_D11

H1_D12

H1_D13

H1_D14

H1_D15

H1_D16

H2_D1

H2_D2

H2_D3

H2_D4

H2_D5

H2_D6

H2_D7

H2_D8

H2_D9

H2_D10

H2_D11

H2_D12

H2_D13

H2_D14

H2_D15

H2_D16

H3_D1

H3_D2

H3_D3

H3_D4

H3_D5

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.00–0.50

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

0.50–1.00

1.00–1.50

1.00–1.50

1.00–1.50

1.00–1.50

1.00–1.50

0.00–22.50

22.50–45.00

45.00–67.50

67.50–90.00

90.00–112.50

112.50–135.00

135.00–157.50

157.50–180.00

180.00–202.50

202.50–225.00

225.00–247.50

247.50–270.00

270.00–292.50

292.50–315.00

315.00–337.50

337.50–360.00

0.00–22.50

22.50–45.00

45.00–67.50

67.50–90.00

90.00–112.50

112.50–135.00

135.00–157.50

157.50–180.00

180.00–202.50

202.50–225.00

225.00–247.50

247.50–270.00

270.00–292.50

292.50–315.00

315.00–337.50

337.50–360.00

0.00–22.50

22.50–45.00

45.00–67.50

67.50–90.00

90.00–112.50

0.62

0.87

0.87

1.24

1.64

2.5

5.07

6.15

3.39

2.38

1.21

0.76

0.63

0.75

0.97

1.2

0.84

0.83

1.97

1.61

3.15

3.3

5.67

5.1

3.85

1.88

1.19

0.55

0.71

0.63

0.67

0.88

1.04

1.06

1.4

1.03

2.38

12/28/2010 9:00

4/10/2012 21:00

10/16/2010 3:00

10/24/2011 6:00

5/27/2010 3:00

4/21/2010 3:00

3/17/2012 0:00

6/26/2011 0:00

8/8/2011 3:00

7/17/2011 15:00

9/27/2011 0:00

3/26/2012 15:00

2/14/2011 9:00

7/15/2010 15:00

7/31/2010 12:00

5/18/2011 12:00

12/2/2010 15:00

2/7/2012 18:00

12/20/2010 9:00

2/9/2011 12:00

5/11/2012 21:00

6/9/2011 18:00

4/4/2010 18:00

4/10/2011 0:00

8/19/2010 18:00

8/9/2011 0:00

4/27/2010 12:00

7/12/2010 12:00

8/27/2011 12:00

8/22/2010 18:00

7/29/2010 18:00

2/12/2011 3:00

12/19/2010 0:00

12/19/2010 15:00

1/3/2011 15:00

4/7/2012 18:00

12/13/2011 9:00
34 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Table 1–1. Wave height and direction scenarios.—Continued

[m, meters; °, degrees; >, greater than]

Scenario Wave height bin, in m Wave direction bin,1 in ° Percentage of 

observations Representative date and time

H3_D6 1.00–1.50 112.50–135.00 2.61 10/6/2011 6:00

H3_D7 1.00–1.50 135.00–157.50 3.65 4/18/2012 9:00

H3_D8 1.00–1.50 157.50–180.00 2.47 4/20/2011 18:00

H3_D9 1.00–1.50 180.00–202.50 1.33 6/22/2011 9:00

H3_D10 1.00–1.50 202.50–225.00 0.61 11/17/2010 12:00

H3_D11 1.00–1.50 225.00–247.50 0.46 10/27/2010 21:00

H3_D12 1.00–1.50 247.50–270.00 0.11 1/29/2011 3:00

H3_D13 1.00–1.50 270.00–292.50 0.15 5/29/2012 15:00

H3_D14 1.00–1.50 292.50–315.00 0.24 1/7/2011 6:00

H3_D15 1.00–1.50 315.00–337.50 0.56 3/11/2011 0:00

H3_D16 1.00–1.50 337.50–360.00 0.99 9/30/2010 6:00

H4_D1 1.50–2.00 0.00–22.50 0.77 12/6/2010 0:00

H4_D2 1.50–2.00 22.50–45.00 0.58 10/30/2011 0:00

H4_D3 1.50–2.00 45.00–67.50 0.34 2/4/2011 0:00

H4_D4 1.50–2.00 67.50–90.00 0.51 7/3/2010 15:00

H4_D5 1.50–2.00 90.00–112.50 1.27 11/6/2011 9:00

H4_D6 1.50–2.00 112.50–135.00 1.38 4/15/2012 9:00

H4_D7 1.50–2.00 135.00–157.50 1.62 12/22/2011 12:00

H4_D8 1.50–2.00 157.50–180.00 1.05 6/29/2010 15:00

H4_D9 1.50–2.00 180.00–202.50 0.44 3/3/2012 15:00

H4_D10 1.50–2.00 202.50–225.00 0.17 12/17/2010 15:00

H4_D11 1.50–2.00 225.00–247.50 0.19 11/29/2011 9:00

H4_D12 1.50–2.00 247.50–270.00 0.05 1/8/2011 6:00

H4_D13 1.50–2.00 270.00–292.50 0.25 11/28/2011 21:00

H4_D14 1.50–2.00 292.50–315.00 0.21 12/27/2011 21:00

H4_D15 1.50–2.00 315.00–337.50 0.34 12/1/2010 6:00

H4_D16 1.50–2.00 337.50–360.00 0.83 1/2/2011 18:00

H5_D1 >2.00 0.00–22.50 0.27 10/29/2011 12:00

H5_D2 >2.00 22.50–45.00 0.14 2/25/2012 15:00

H5_D3 >2.00 45.00–67.50 0.11 12/11/2011 6:00

H5_D4 >2.00 67.50–90.00 0.37 7/3/2010 21:00

H5_D5 >2.00 90.00–112.50 0.66 10/8/2011 18:00

H5_D6 >2.00 112.50–135.00 0.98 3/4/2011 0:00

H5_D7 >2.00 135.00–157.50 1.27 11/27/2011 12:00

H5_D8 >2.00 157.50–180.00 1.13 5/3/2010 12:00

H5_D9 >2.00 180.00–202.50 0.48 9/5/2011 9:00

H5_D10 >2.00 202.50–225.00 0.16 12/16/2010 21:00

H5_D11 >2.00 225.00–247.50 0.07 1/11/2012 15:00

H5_D12 >2.00 247.50–270.00 0.02 1/8/2011 6:00

H5_D13 >2.00 270.00–292.50 0.15 12/27/2011 12:00

H5_D14 >2.00 292.50–315.00 0.27 12/12/2010 15:00

H5_D15 >2.00 315.00–337.50 0.31 12/13/2010 6:00

H5_D16 >2.00 337.50–360.00 0.47 4/22/2012 9:00

1

Indicates the direction of the waves, in degrees from north.
Appendix 1. Scenarios 35

The period chosen to represent each scenario was identified by matching the multivariate wave height and direction of 

that scenario to the values defining each bin. The match was 

made by evaluating the likelihood of each observation given 

the bin-defining values. Observations were given an uncertainty equal to 0.1 times the width of the bin to allow matching 

observations that fall on bin boundaries. It is expected that 

the best-match scenario would come from a short time period 

(6 hours) where the conditions consistently met the scenario 

conditions in order to avoid choosing transitional conditions 

that may produce unrepresentative conditions. The comparison of the best match to the H3_D8 scenario shows that this 

approach effectively selected time periods with representative 

wave period and offshore wind conditions (fig. 1–2).

Figure 1–1. Example of a 

scenario H3_D8 with wave 

height of 1.25 meters and wave 

direction of 169 degrees. Red 

bars show the normalized 

distribution of other relevant 

variables, constrained by 

height and direction: A, Wave 

height; B, Wave direction; C, 

Wave period; D, Wind speed; 

and, E, Wind direction. Blue 

dots show the data for the 

observation times that fall 

within this scenario.
36 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Figure 1–2. Comparison of the best-match condition (yellow dot) to the target values for the scenario (magenta asterisk) against all 

observations (blue dots) for scenario H3_D8. A, wave height and direction, B, wind speed and wave direction, and C, wave height and 

period.
Appendix 2. Examples of Input Files for the Model 37

Appendix 2. Examples of Input Files for the Model

Files for FLOW (flow.mdf) and WAVE (wave.mdw) 

modules can be found with the digital version of this report.

Flow Input File

Ident = #Delft3D-FLOW .03.02 

3.42.00.17790#

Commnt =

Filcco = #OSAT3_D3D_edit9_UTM.grd#

Filgrd = #OSAT3_D3D_edit9_UTM.enc#

MNKmax = 1037 968 1

Thick = 1.0000000e+002

Commnt =

Fildep = #OSAT3_D3D_edit9.dep#

Commnt =

Commnt = no. dry points: 0

Commnt = no. thin dams: 0

Commnt =

Itdate = #2010-12-28#

Tunit = #M#

Tstart = 5.4000000e+02

Tstop = 9.0000000e+02

Dt = 1

Tzone = 0

Commnt =

Sub1 = # W #

Sub2 = # W#

Commnt =

Wnsvwp = #N#

Filwnd = #temp.wnd#

Wndint = #Y#

Commnt =

Zeta0 = 0.0000000e+000

Commnt =

Commnt = no. open boundaries: 3

Filbnd = #scenarios.bnd#

FilbcH = #scenarios.bch#

Commnt =

Ag = 9.8100000e+000

Rhow = 1.0000000e+003

Tempw = 1.5000000e+001

Salw = 3.1000000e+001

Rouwav = #FR84#

Wstres = 6.3000000e-004 

0.0000000e+000 7.2300000e-003 

1.0000000e+002 7.2300000e-003 

1.0000000e+002

Rhoa = 1.0000000e+000

Betac = 5.0000000e-001

Equili = #N#

Ktemp = 0

Fclou = 0.0000000e+000

Sarea = 0.0000000e+000

Temint = #Y#

Commnt =

Roumet = #C#

Ccofu = 6.5000000e+001

Ccofv = 6.5000000e+001

Xlo = 0.0000000e+000

Vicouv = 1.0000000e+000

Dicouv = 1.0000000e+001

Htur2d = #N#

Irov = 0

Commnt =

Iter = 2

Dryflp = #YES#

Dpsopt = #MAX#

Dpuopt = #MEAN#

Dryflc = 1.0000000e-001

Dco = -9.9900000e+002

Tlfsmo = 6.0000000e+001

ThetQH = 0.0000000e+000

Forfuv = #Y#

Forfww = #N#

Sigcor = #N#

Trasol = #Cyclic-method#

Momsol = #Cyclic#

Commnt =

Commnt = no. discharges: 0

Commnt = no. observation points: 3

Filsta = #tide.obs#

Commnt = no. drogues: 0

Commnt =

Commnt =

Commnt = no. cross sections: 0

Commnt =

SMhydr = #YYYYY#
38 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

SMderv = #YYYYYY#

SMproc = #YYYYYYYYYY#

PMhydr = #NNNNNN#

PMderv = #NNN#

PMproc = #NNNNNNNNNN#

SHhydr = #YYYY#

SHderv = #YYYYY#

SHproc = #YYYYYYYYYY#

SHflux = #YYYY#

PHhydr = #NNNNNN#

PHderv = #NNN#

PHproc = #NNNNNNNNNN#

PHflux = #NNNN#

Online = #N#

Waqmod = #N#

WaveOL = #Y#

Flmap = 5.4000000e+02 60 

9.0000000e+02

Flhis = 5.4000000e+02 10 

9.0000000e+02

Flpp = 5.4000000e+02 360 

9.0000000e+02

Flrst = 360

Commnt =

Fwndgp = wind.amp

Fwndgu = wind.amu

Fwndgv = wind.amv

Commnt =

Wave Input File

[WaveFileInformation]

FileVersion = 02.00

[General]

FlowFile = flow.mdf

OnlyInputVerify = false

SimMode = stationary

DirConvention = nautical

ReferenceDate = 2010-12-28

WindSpeed = 0.0000000e+000

WindDir = 0.0000000e+000

[Constants]

WaterLevelCorrection = 

0.0000000e+000

Gravity = 9.8100004e+000

WaterDensity = 1.0250000e+003

NorthDir = 9.0000000e+001

MinimumDepth = 5.0000001e-002

[Processes]

GenModePhys = 3

Breaking = true

BreakAlpha = 1.0000000e+000

BreakGamma = 7.3000002e-001

Triads = false

TriadsAlpha = 1.0000000e-001

TriadsBeta = 2.2000000e+000

BedFriction = jonswap

BedFricCoef = 6.7000002e-002

Diffraction = false

DiffracCoef = 2.0000000e-001

DiffracSteps = 5

DiffracProp = true

WindGrowth = true

WhiteCapping = Komen

Quadruplets = true

Refraction = true

FreqShift = true

WaveForces = radiation stresses

[Numerics]

DirSpaceCDD = 5.0000000e-001

FreqSpaceCSS = 5.0000000e-001

RChHsTm01 = 2.0000000e-002

RChMeanHs = 2.0000000e-002

RChMeanTm01 = 2.0000000e-002

PercWet = 9.5000000e+001

MaxIter = 10

[Output]

TestOutputLevel = 0

TraceCalls = false

UseHotFile = false

MapWriteInterval = 0.0000000e+000

WriteCOM = true

COMWriteInterval = 3.6000000e+002

LocationFile = buoy.loc

WriteTable = true

WriteSpec1D = false

WriteSpec2D = false

[Domain]

Grid = OSAT3_D3D_edit9_UTM.grd

FlowBedLevel = 0

FlowWaterLevel = 0

FlowVelocity = 0

FlowWind = 2

BedLevel = OSAT3_D3D_edit9.dep
Appendix 2. Examples of Input Files for the Model 39

DirSpace = circle

NDir = 72

FreqMin = 5.0000001e-002

FreqMax = 1.0000000e+000

NFreq = 24

Output = true

[Boundary]

Name = Bound1

Definition = grid-coordinates

StartCoordM = 0

EndCoordM = 0

StartCoordN = 0

EndCoordN = 29

SpectrumSpec = from file

Spectrum = TPAR1.bnd

[Boundary]

Name = Bound2

Definition = grid-coordinates

StartCoordM = 0

EndCoordM = 0

StartCoordN = 29

EndCoordN = 59

SpectrumSpec = from file

Spectrum = TPAR2.bnd

[Boundary]

Name = Bound3

Definition = grid-coordinates

StartCoordM = 0

EndCoordM = 1020

StartCoordN = 59

EndCoordN = 179

SpectrumSpec = from file

Spectrum = TPAR3.bnd

[Boundary]

Name = Bound4

Definition = grid-coordinates

StartCoordM = 1020

EndCoordM = 1020

StartCoordN = 179

EndCoordN = 149

SpectrumSpec = from file

Spectrum = TPAR4.bnd

[Boundary]

Name = Bound5

Definition = grid-coordinates

StartCoordM = 1020

EndCoordM = 1020

StartCoordN = 149

EndCoordN = 119

SpectrumSpec = from file

Spectrum = TPAR5.bnd

[Boundary]

Name = Bound6

Definition = grid-coordinates

StartCoordM = 1020

EndCoordM = 1020

StartCoordN = 119

EndCoordN = 89

SpectrumSpec = from file

Spectrum = TPAR6.bnd

[Boundary]

Name = Bound7

Definition = grid-coordinates

StartCoordM = 1020

EndCoordM = 1020

StartCoordN = 89

EndCoordN = 59

SpectrumSpec = from file

Spectrum = TPAR7.bnd

[Boundary]

Name = Bound8

Definition = grid-coordinates

StartCoordM = 1020

EndCoordM = 1020

StartCoordN = 59

EndCoordN = 29

SpectrumSpec = from file

Spectrum = TPAR8.bnd

[Boundary]

Name = Bound9

Definition = grid-coordinates

StartCoordM = 1020

EndCoordM = 1020

StartCoordN = 29

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR9.bnd

[Boundary]

Name = Bound10

Definition = grid-coordinates

StartCoordM = 1020

EndCoordM = 1020

StartCoordN = 0

EndCoordN = 0
40 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

SpectrumSpec = from file

Spectrum = TPAR10.bnd

[Boundary]

Name = Bound11

Definition = grid-coordinates

StartCoordM = 1020

EndCoordM = 989

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR11.bnd

[Boundary]

Name = Bound12

Definition = grid-coordinates

StartCoordM = 989

EndCoordM = 959

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR12.bnd

[Boundary]

Name = Bound13

Definition = grid-coordinates

StartCoordM = 959

EndCoordM = 929

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR13.bnd

[Boundary]

Name = Bound14

Definition = grid-coordinates

StartCoordM = 929

EndCoordM = 899

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR14.bnd

[Boundary]

Name = Bound15

Definition = grid-coordinates

StartCoordM = 899

EndCoordM = 869

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR15.bnd

[Boundary]

Name = Bound16

Definition = grid-coordinates

StartCoordM = 869

EndCoordM = 839

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR16.bnd

[Boundary]

Name = Bound17

Definition = grid-coordinates

StartCoordM = 839

EndCoordM = 809

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR17.bnd

[Boundary]

Name = Bound18

Definition = grid-coordinates

StartCoordM = 809

EndCoordM = 779

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR18.bnd

[Boundary]

Name = Bound19

Definition = grid-coordinates

StartCoordM = 779

EndCoordM = 749

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR19.bnd

[Boundary]

Name = Bound20

Definition = grid-coordinates

StartCoordM = 749

EndCoordM = 719

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR20.bnd

[Boundary]

Name = Bound21
Appendix 2. Examples of Input Files for the Model 41

Definition = grid-coordinates

StartCoordM = 719

EndCoordM = 689

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR21.bnd

[Boundary]

Name = Bound22

Definition = grid-coordinates

StartCoordM = 689

EndCoordM = 659

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR22.bnd

[Boundary]

Name = Bound23

Definition = grid-coordinates

StartCoordM = 659

EndCoordM = 629

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR23.bnd

[Boundary]

Name = Bound24

Definition = grid-coordinates

StartCoordM = 629

EndCoordM = 599

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR24.bnd

[Boundary]

Name = Bound25

Definition = grid-coordinates

StartCoordM = 599

EndCoordM = 539

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR25.bnd

[Boundary]

Name = Bound26

Definition = grid-coordinates

StartCoordM = 539

EndCoordM = 509

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR26.bnd

[Boundary]

Name = Bound27

Definition = grid-coordinates

StartCoordM = 509

EndCoordM = 479

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR27.bnd

[Boundary]

Name = Bound28

Definition = grid-coordinates

StartCoordM = 479

EndCoordM = 449

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR28.bnd

[Boundary]

Name = Bound29

Definition = grid-coordinates

StartCoordM = 449

EndCoordM = 419

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR29.bnd

[Boundary]

Name = Bound30

Definition = grid-coordinates

StartCoordM = 419

EndCoordM = 389

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR30.bnd

[Boundary]

Name = Bound31

Definition = grid-coordinates

StartCoordM = 389

EndCoordM = 359

StartCoordN = 0
42 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR31.bnd

[Boundary]

Name = Bound32

Definition = grid-coordinates

StartCoordM = 359

EndCoordM = 329

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR32.bnd

[Boundary]

Name = Bound33

Definition = grid-coordinates

StartCoordM = 329

EndCoordM = 299

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR33.bnd

[Boundary]

Name = Bound34

Definition = grid-coordinates

StartCoordM = 299

EndCoordM = 269

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR34.bnd

[Boundary]

Name = Bound35

Definition = grid-coordinates

StartCoordM = 269

EndCoordM = 239

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR35.bnd

[Boundary]

Name = Bound36

Definition = grid-coordinates

StartCoordM = 239

EndCoordM = 209

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR36.bnd

[Boundary]

Name = Bound37

Definition = grid-coordinates

StartCoordM = 209

EndCoordM = 179

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR37.bnd

[Boundary]

Name = Bound38

Definition = grid-coordinates

StartCoordM = 179

EndCoordM = 149

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR38.bnd

[Boundary]

Name = Bound39

Definition = grid-coordinates

StartCoordM = 149

EndCoordM = 119

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR39.bnd

[Boundary]

Name = Bound40

Definition = grid-coordinates

StartCoordM = 119

EndCoordM = 89

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR40.bnd

[Boundary]

Name = Bound41

Definition = grid-coordinates

StartCoordM = 89

EndCoordM = 59

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR41.bnd

[Boundary]
Appendix 2. Examples of Input Files for the Model 43

Name = Bound42

Definition = grid-coordinates

StartCoordM = 59

EndCoordM = 29

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR42.bnd

[Boundary]

Name = Bound43

Definition = grid-coordinates

StartCoordM = 29

EndCoordM = 0

StartCoordN = 0

EndCoordN = 0

SpectrumSpec = from file

Spectrum = TPAR43.bnd
44 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Appendix 3. Calculations of Mobility and Potential Flux

Shear Stress Calculated From Hydrodynamic 

Model Output

In order to estimate mobility, the combined wave-current 

shear stress must be calculated for the modeled hydrodynamic 

conditions. A formulation was developed by Soulsby (1997) to 

parameterize four methods, which provide good overall performance for estimating wave-current stress, based on original 

formulations by Grant and Madsen (1979), Fredsøe (1984), 

Davies and others (1988), and Huynh-Thanh and Temperville 

(1991). The combined wave-current stress (τwc) for the individual components of wave and current stress was calculated 

for hydrodynamic model output (depth-averaged velocity 

magnitude and direction, wave bottom orbital velocity, wave 

period, wave direction, and water depth) following the method 

prescribed in Soulsby (1997) for each of the four formulations. 

The density of water used in the calculations was as assumed 

to be 1,027 kilograms per cubic meter (kg/m3

), and the grainsize roughness contribution (z0

) was calculated to be (Soulsby, 

1997) the diameter of the particle (either surface residual ball 

(SRB) or surficial sediment) divided by 12. The mean value 

of the four formulations was used to estimate the combined 

wave-current shear stress for each hydrodynamic scenario and 

for all time-steps of the time varying simulations. Evaluation 

of the standard deviation of the four methods indicated the 

uncertainty introduced by calculation method is low compared with the magnitude of the calculated stress (less than 1 

percent).

Critical Stress for Incipient Motion

Most research into critical thresholds for incipient motion 

of noncohesive sediment (including large grains such as gravel 

and cobbles, in a similar size range to SRBs) has at least partial basis in the work of Shields (1936) who created a dimensionless parameter (θcr) based on the shear stress (τcr). The 

shear stress balances the gravitational weight of the particle 

(described in Soulsby, 1997):

θ τ

ρ ρ cr

cr

s g d = ( ) − , (3–1)

where

g is the acceleration due to gravity (9.81 meters 

per second squared (m/s2)),

	 ρs is the density of the sediment, 

ρ is the density of water, and

d is the diameter of the grain of the sediment.

Soulsby empirically determined the relation between this critical value and the grain diameter and density; the equation was 

subsequently updated by Soulsby and Whitehouse (1997) to 

cover a wider range of conditions.

cr D = D

+

+ −  ( ) −  



0 30

1 1 2

0 055 1 0 020 .

. . exp .

*

*

, (3–2)

where D* is the dimensionless grain size, calculated as 

follows:

D

g

v

d

s

* =

− 



 

































1

2

1

3

, (3–3)

where ν is the kinematic viscosity of water, 1.36×10-6 m2/s.

The high critical stress estimate for each SRB class (and 

the only critical stress value used for sand) was attained by 

replacing θcr in equation 3–1 with the value of θcr from equation 3–2 and solving for τcr; the estimate is appropriate for 

the conditions for which the formulation was calibrated, for 

example, particles not protruding above the bed into the flow.

Experiments have demonstrated that the extent to which 

any individual particle protrudes from the bed (such as could 

be expected for a single SRB on a seabed of sand) can lower 

that particle’s critical shear stress (τcr) value (Fenton and 

Abbott, 1977; Andrews, 1983; Wiberg and Smith, 1987; 

Wilcock, 1998; Bottacin-Busolin and others, 2008). Empirical studies of cobbles have indicated that the dimensionless 

critical shear stress (θcr) approaches a minimum value of 0.01 

to 0.02 (Fenton and Abbott, 1977; Andrews, 1983; Wiberg 

and Smith, 1987; Wilcock, 1998; Bottacin-Busolin and others, 2008). Note that, although the dimensionless Shields 

parameter θcr is constant for the exposed particle stress case, 

the conversion to the physically meaningful force (in pascals) 

includes a dependence on grain size; thus, the critical stress 

compared with modeled stress forcing increases for large 

particles. For the analysis of SRB mobility, when particle 

extrusion is important, the critical stress value is calculated 

from a θcr of 0.02 (medium threshold) and 0.01 (low threshold) 

to provide a limit on the uncertainty in mobility for the range 

of conditions from an SRB in a relatively uniform bed of 

SRBs such as a mat (for example, little particle extrusion) to 

an isolated SRB sitting relatively high in the flow.

SRB Density

For sediment mixed with oil, Operational Science 

Advisory Team (OSAT3) data were used to constrain the den-
Appendix 3. Calculations of Mobility and Potential Flux 45

sity of observed SRBs (L. Bruce, British Petroleum Corporation, GCRO, Science NRDA Team, unpub. data, 2012). Composition data provide the percentage of moisture (fH2O) and the 

percentage of oil by dry weight (foil,dry) of the sampled SRBs; 

the total percentage of oil of the original (wet weight) sample 

is taken as foil = (1 – fH2O) × foil,dry. To estimate the density of 

the samples, an assumed density of 1,027 kg/m3 was assigned 

to the moisture fraction, an assumed density of 900 kg/m3 was 

assigned to the oil fraction, and the remaining fraction of 1 – 

fH2O – (1 – fH20) × foil,dry was assumed to consist of quartz sand 

with a density of 2,650 kg/m3. The approximate density (ρSRB) 

of each sample in the dataset was therefore estimated to be:

SRB

H O H O oil dry HO HO oil d f f f f f f = + − × + − − − × 2 2 2 2

1 027

1

900

1 1

,

( ) ( ) , , ry

2 650

1

,













−

, (3–4)

The densities calculated in this manner for all the 

observed SRB data were used in assessing the variability of 

SRB critical stress.
46 Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response

Appendix 4. File Naming Conventions

The analyses described in the Methods section of this 

report have been applied for each wave scenario to determine 

patterns in alongshore currents, movement probability for 

surface residual balls (SRBs) and sediment, and probable 

alongshore redistribution patterns for SRBs of mobilized size 

classes. These results are available in geographic information 

systems (GIS) polygon or point shapefile format, with all files 

for a given scenario having a prefix of Hh_Dd, where h and 

d denote the scenario wave height (H) and direction (D) bin 

number, respectively. So, for example, a prefix of “H1_D1” 

corresponds to a wave height in the lowest bin (0.0 to 0.5 m) 

and wave direction in the first bin (0 to 22.5 degrees). A table 

of scenario characteristics is provided in appendix 1 and is 

also included in a text file (.txt) zipped with each GIS shapefile. For SRB and sediment analyses, each shapefile includes 

results for each of the six SRB size classes and critical stress 

values described in table 1 of this report (also included zipped 

with each GIS shapefile). The final portion of the filename 

denotes the analysis type as described in table 2 in the Methods section of this report. For example, H1_D1_mobility.

xxx would contain mobility analysis for scenario H1_D1 for 

sediment and each size and critical stress level for SRBs, with 

various file extensions (.xxx) associated with the GIS shapefile.

In addition to the GIS shapefiles, animations were created 

of the mobility of 2.5-cm SRBs (size class 4) and sand over a 

tidal cycle for three inlets: Pensacola Pass, Fla.; Little Lagoon, 

Ala.; and Panama City, Fla. These files follow the naming convention [InletName]_SRB.avi and [InletName]_sediment.avi.
Appendix 5. Time Step of Maximum Ebb and Flood for Inlets in the Model Domain 47

Appendix 5. Time Step of Maximum Ebb and Flood for Inlets in the Model 

Domain

The time of maximum ebb and maximum flood varies 

for each inlet within the model domain. Table 5–1 provides 

the time step index and thus the corresponding GIS file of 

maximum flood and ebb for each inlet, defined as the time step 

corresponding to the maximum flow into and out of the inlet, 

respectively, in the center of the inlet for scenario H4_D7.

Table 5–1. Time step index corresponding to maximum flood and ebb for inlets within the model 

domain. 

[The time step (TT) indicates the file naming convention for files in the geographic information system of this report, 

where files naming convention follows the pattern TT_mobility.xxx; xxx indicates the file format]

Inlet Latitude Longitude Maximum flood TT Maximum ebb TT

Mobile Bay, Alabama30.2253 -88.0381 8 18

Little Lagoon, Ala. 30.2405 -87.7377 11 23

Perdido Pass, Ala. 30.2724 -87.5594 10 18

Pensacola Pass, 

Florida

30.3210 -87.3083 7 19

Destin, Fla. 30.3847 -86.5080 10 22

Panama City, Fla. 30.1212 -85.7327 7 18


Plant and Others—Application of Hydrodynamic and Sediment Transport Model for Deepwater Horizon Oil Spill Response—Open-File Report 2012-1234