Documentation of the U.S. Geological Survey Sea Floor Stress 

and Sediment Mobility Database

Open-File Report 2012-1137

U.S. Department of the Interior

U.S. Geological Survey

Documentation of the U.S. Geological Survey Sea Floor 

Stress and Sediment Mobility Database

By P. Soupy Dalyander, Bradford Butman, Christopher R. Sherwood, and Richard P. Signell

Open-File Report 2012-1137

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012

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Suggested citation:

Dalyander, P.S., Butman, Bradford, Sherwood, C.R., and Signell, R.P., 2012, Documentation 

of the U.S. Geological Survey Stress and Sediment Mobility Database: U.S. Geological Survey Open-File 

Report 2012–1137, 20 p., available at http://pubs.usgs.gov/of/2012/1137/

Any use of trade, product, or firm names is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual 

copyright owners to reproduce any copyrighted material contained within this report.
iii

Contents

Abstract ...................................................................................................................................................................... 1

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

Estimation of Bottom Stress........................................................................................................................................ 1

Stress Characterizations............................................................................................................................................. 3

Bed Mobility Characterization ..................................................................................................................................... 3

Contents of the Sea Floor Stress and Sediment Mobility Database ........................................................................... 5

Data Format................................................................................................................................................................ 5

Metadata..................................................................................................................................................................... 5

Data Validation ........................................................................................................................................................... 6

Data Review ............................................................................................................................................................... 6

Database Access via the Web.................................................................................................................................... 6

Acknowledgments....................................................................................................................................................... 6

Selected References .................................................................................................................................................. 7

Glossary ..................................................................................................................................................................... 9

Tables

1. Example statistics included in the U.S. Geological Survey Sea Floor Stress and Sediment Sediment 

Mobility Database. ......................................................................................................................................... 5
iv

Conversion Factors

SI to Inch/Pound

Multiply By To obtain

Length

meter (m) 3.281 foot (ft) 

Acceleration

meter per second squared (m/s2) 3.281 foot per second squared (ft/s2)

Kinematic viscosity

meters squared per second (m2/s) 10.765 feet squared per second (ft2/s)

Pressure

kilopascal (kPa) 20.88 pound per square foot (lb/ft2) 

Density

kilogram per cubic meter (kg/m3) 0.06242 pound per cubic foot (lb/ft3) 
1

Documentation of the U.S. Geological Survey Sea Floor 

Stress and Sediment Mobility Database

By P. Soupy Dalyander, Bradford Butman, Christopher R. Sherwood, and Richard P. Signell

Abstract

The U.S. Geological Survey Sea Floor Stress and Sediment Mobility Database contains 

estimates of bottom stress and sediment mobility for the U.S. continental shelf. This U.S. Geological 

Survey database provides information that is needed to characterize sea floor ecosystems and evaluate 

areas for human use. The estimates contained in the database are designed to spatially and seasonally 

resolve the general characteristics of bottom stress over the U.S. continental shelf and to estimate sea 

floor mobility by comparing critical stress thresholds based on observed sediment texture data to the 

modeled stress. This report describes the methods used to make the bottom stress and mobility 

estimates, statistics used to characterize stress and mobility, data validation procedures, and the 

metadata for each dataset and provides information on how to access the database online.

Introduction

Ocean waves and currents create bottom shear stress, a force at the seabed that influences 

physical, geological, and biological processes and thus is important in evaluating sites for offshore 

structures, understanding the distribution of toxic materials, and predicting the distribution of seabed 

plants and animals. The growing requirement for shear stress information across broad planning regions 

on the U.S. continental shelf cannot be met by direct measurements of bottom shear stress, which are 

expensive. Instead, wave and current output from numerical models can be used in a bottom boundary 

layer model to produce estimates of bottom stress across the continental shelf. These estimates are used 

to create the U.S. Geological Survey (USGS) Sea Floor Stress and Sediment Mobility Database, which 

contains statistical characterizations of bottom stress and sediment mobility for the U.S. continental 

shelf.

This report describes the methods used to make the bottom stress and mobility estimates, 

statistics used to characterize stress and mobility, data validation procedures, and the metadata for each 

dataset and provides instructions on how to access the data from the online database. Estimates of 

bottom stress and mobility will be added to the online database as they are developed.

Estimation of Bottom Stress

Bottom shear stress estimates are made following the Grant-Madsen (GM) model (Madsen, 

1994), with bottom orbital velocity and bottom wave periods generated with third generation wave 

models (such as Simulation WAves Nearshore, SWAN; Holthuijsen and others, 1993) and near-bed 

current estimates from three-dimensional spatially and temporally resolved hydrodynamic models (such 

as the Regional Ocean Modeling System, ROMS; Shchepetkin and McWilliams, 2005). The bottom 

stress estimates are provided on a kilometer-scale grid matching the grid of the hydrodynamic model. 
2

The GM approach relies on an eddy viscosity turbulence closure model and formulates the wave stress 

(τwave), current stress (τcurr), and combined wave-current bottom stress (τwc) as functions of a 

representative bottom wave orbital velocity (ubr), representative bottom wave period (Tbr), current flow 

at some reference height, the angle between wave and current propagation, and bottom roughness (kb). 

Full details of the GM formulation may be found in Glenn (1983), Grant and Madsen (1979, 1982, 

1986), Glenn and Grant (1987), Madsen and others (1988), and Madsen (1994).

Wave direction, bottom orbital velocities, and bottom periods are calculated internally by the 

wave model. Near-bed current magnitude and direction are taken from the hydrodynamic model, with 

the reference height (zR) taken as the distance from the cell vertical midpoint to the seabed. The GM 

model requires that the current velocity be taken above the wave boundary layer (WBL) but within the 

log-profile current velocity layer. If the thickness of the WBL (δw) calculated using the GM model 

exceeds the zR of one or more of the deepest grid cells, then the current estimate and associated 

reference height are used from the deepest grid cell at each location where zR exceeds δw. An estimate 

must be used for the maximum reference height where the log-profile velocity layer assumption is valid. 

As discussed in Grant and Madsen (1986), the thickness of the log-profile layer based on laboratory 

experiments is approximately 10 percent of the current boundary layer thickness (Clauser, 1956). 

Because tidal currents, storm currents, and mean flow have a boundary layer thickness on the order of a 

magnitude of tens of meters (Goud, 1987), a maximum value for zR is set as 5 meters (m). This value 

may overestimate the thickness of the log layer in some flow conditions; in-situ measurements of the 

near-bed profile have found some deviation from a log-profile at distances less than 5 m off the bed 

(Sanford and Lien, 1999).

The GM bottom boundary layer model also requires a value for bottom roughness; a uniform 

value of 0.005 m is used throughout the domain. The physical roughness used in stress calculations is 

the Nikuradse sand grain size (kb, a measurement of roughness), which includes contributions from 

bedform microtopography (Nikuradse, 1933; Madsen, 1994). However, even if sediment grain size were 

an adequate proxy for bottom roughness and grain size data at kilometer-scale were available, defining a 

single roughness for each grid cell would be nonphysical in many regions because of finer scale spatial 

variability in sediment texture (Churchill and others, 1994). Bedform microtopography also exhibits 

finer scale spatial variability as well as time variability that includes a dependence on bottom stress. 

When the critical stress of motion is exceeded on a sandy seabed, ripples will start to form, which 

enhance the roughness (Glenn, 1983; Glenn and Grant, 1987). Ripple characteristics vary with flow 

conditions, with ripples steepening under increased bottom orbital velocities until the “breakoff region” 

is entered and ripples begin to be smoothed out or destroyed (Grant and Madsen, 1986). Accounting for 

these processes is difficult because the seabed may not be in equilibrium with flow conditions due to 

relic bedforms. Bedforms may also be formed or destroyed through bioturbation or anthropogenic 

activity, such as trawling. During nonstorm conditions, particularly in muddy sediments, biological 

activity can influence or dominate the microtopography (Grant and Madsen, 1986). In addition, 

nongeological elements, such as shell hash or submerged aquatic vegetation (SAV), will influence the 

roughness. There is also a contribution of sediment being transported near the seabed to the total bottom 

roughness (Glenn, 1983), which itself is difficult to compute due to the influence of stress history on 

sediment resuspension (for example, bed armoring) and sediment advection from other locations. Over 

smaller study areas, these problems may be addressed through direct observation and estimation of the 

bottom roughness (Lyne and others, 1990a,b). Use of a uniform value of 0.005 m most likely 

underestimates the roughness and hence the stress for sandy seabeds during moderate storm conditions 

when ripples develop, but based on sea floor observations (Grant and Madsen, 1986; Lyne and others, 

1990a,b) is a reasonable estimate during more extreme storms when ripples flatten, during quiescent 
3

periods if relict bedforms are absent, and over muddy seabeds where ripples do not form. Additional 

influences of biological and anthropogenic forces on roughness are difficult to spatially or temporally 

resolve. Use of a uniform value of 0.005 m for bottom roughness produces a small relative error in the 

calculated stress, which varies with the natural logarithm of kb (Madsen and others, 1993).

Stress Characterizations

Stress characterizations are resolved for each model grid cell both annually and seasonally, for 

example, winter (December-February), spring (March-May), summer (June-August), and fall 

(September-November). Where time series of bottom stress longer than a year are available, estimates 

of interannual variability are also provided.

The baseline set of statistics used to characterize stress spatially and temporally include (Table 1):

• Median: the value for which 50 percent of stress estimates fall below and 50 percent of stress 

estimates fall above (equivalent to the mean for a normal distribution)

• Half interpercentile range: half of the difference between the 84th and 16th percentiles 

(equivalent to the standard deviation for a normal distribution)

• 95th percentile: the value exceeded by 5 percent of data in the time series (for example, 95 

percent of output points are less than this value)

Bed Mobility Characterization

Bed mobility is assessed at discrete locations by comparing bottom stress to grain-size specific 

critical stress thresholds established using observed surficial sediment texture point measurements. Bed 

mobility is established as the percentage of time the critical stress at the location of each sample is 

exceeded for that sample; a yearly bed mobility of 20 percent would indicate the bed is mobilized 20 

percent of the year. While bed mobility occurrence defined in this manner indicates the overall potential 

for sediment movement throughout the year, it does not characterize the frequency of mobility (for 

example, a mobility of 25 percent could indicate a 6 hour daily disturbance, or 100 percent disturbance 

over 3 months of the year). To characterize frequency, the recurrence interval of mobility events (in 

units of days between events) is calculated for the winter and summer as the total length of the time 

series (in days) divided by the number of events within the time period. A recurrence interval of 10 

days, for example, would indicate that, on average, the bed is mobilized every 10 days. The bed 

mobility statistics are therefore (Table 1):

• Bed mobility percentage: percentage of time the critical stress threshold is exceeded at each 

location

• Bed mobility recurrence interval: total number of mobility events divided by the total length of 

the time series, in days

The total bottom stress as calculated previously is an estimate of the total force in the bottom 

boundary layer, based on a uniform roughness value of 0.005 m that includes a bedform contribution to 

roughness. Seawater in the bottom boundary layer responds to stress resulting from both the form drag 

of microtopography as well as the skin friction of the sediment boundary, but seafloor sediment only 

responds to the skin friction. Use of the total bottom boundary layer stress would overestimate the force 

acting on the sand grains to potentially induce resuspension and transport (Zhenlin Li, 1994). At each 

discrete location where sediment data were available, bottom stress was recalculated from wave and 

circulation model output using the GM method and a roughness (kb) based on the grain size distribution 

at that location. While there are other methodologies that allow the skin friction to be partitioned from 

total boundary layer stress (see Churchill and others, 1994), in this case, the total boundary layer stress 
4

is based on an assumed rather than an observed bedform roughness, and partitioning would therefore not 

improve the estimate of the skin friction compared with basing the roughness on the sediment grain size 

distribution.

The texture data include the distribution of sediment over grain size classes ranging from -5 to 

11 phi (φ), ranging from gravel through sand and silt to clay. For sand grains, there is an established 

positive correlation between critical stress and sediment grain size (Soulsby, 1997). However, mixed 

beds with a high fraction of fine-grained sediments act cohesively, increasing the critical stress 

(Panagiotopoulos and others, 1997; Torfs and others, 2000; van Ledden and others, 2004). Texture 

observations are therefore classified as cohesive or noncohesive based on the fraction of clay; if the clay 

fraction exceeds 7.5 percent, then the sediment is deemed cohesive; if less than or equal to 7.5 percent, 

then the sediment is noncohesive. This classification was based on the mean value from laboratory 

testing that indicates the threshold to develop cohesive properties is between 5 and 10 percent clay (van 

Ledden and others, 2004).

Critical stress thresholds (τcr) for noncohesive sediment mixtures are calculated from the critical 

Shields parameter (θcr), gravity (g, 9.81 meters per second squared (m/s2)), the density of sediment (ρs, 

taken as 2,650 kilograms per cubic meter (kg/m3)), the density of seawater (ρ, taken as 1,027 kg/m3), 

and the median grain size (d50) following Soulsby (1997) as

( ) cr θ cr ρ s ρ d50 τ = ⋅ − (1)

The critical Shields parameter is calculated from a dimensionless sediment parameter, D*, as

0.055[1 exp( 0.020 *)] 1 1.2 *

0.30 D

D cr + − − +

θ = (2)

with D* defined from the kinematic viscosity (v, taken as 1.36×10-5 meters squared per second (m

2

/s))

as

3

1

50 2

* 



 



 ∆ = v

g D d (3)

The roughness used in calculating bottom stress at locations with a noncohesive sediment distribution 

was also set to d50.

For cohesive beds, the critical stress threshold is more difficult to establish. Particle cohesion 

strength, and hence critical stress, varies with fluid properties, such as salinity and temperature; 

sediment matrix properties, including the texture distribution, chemical composition, and water content; 

and biological influences, such as pelletization, organic content, and bioturbidity (Dickhudt and others, 

2011). Furthermore, as the bed erodes, the critical shear stress may increase (for example, bed armoring) 

as older sediment layers with different properties are exposed (van Ledden and others, 2004). Because, 

at present, data do not exist to support a more complex model of critical stress as a function of these 

varying properties, a single value is used for all samples identified as cohesive. In-situ, ex-situ, and

laboratory experimental measurements of critical stress in mixed beds range from 0.01 to 0.7 pascal (Pa) 

(see Dickhudt and others, 2011, for a review). Because the primary interest of this study is initiation of 

bed mobility, a value of 0.1 Pa is chosen. The roughness used in the skin friction calculation for 

cohesive sediments was set to 62.5 micrometers (μm; 4 φ, the boundary between very fine sand and 

coarse silt), which has a critical stress based on Soulsby (1997) of 0.1 Pa. Since different values may be 

appropriate for different regions, the threshold value for cohesive sediments is included in the metadata 

for each set.
5

Contents of the Sea Floor Stress and Sediment Mobility Database

The USGS Sea Floor Stress and Sediment Mobility Database consists of a set of statistics that 

spatially and temporally characterize stress and bed mobility (table 1). Analysis suggests that the 

available models provide reasonable statistics but that individual stress events are not well-resolved. 

Statistics of bottom stress and mobility are therefore included in the database, but the time series of 

bottom stress used to develop these statistics are not.

Table 1. Example statistics included in the U.S. Geological Survey Sea Floor Stress and Sediment Sediment 

Mobility Database.

[See “Stress Characterizations” and “Bed Mobility Characterizations” sections in this report for more complete descriptions 

of how each statistic is computed from bottom stress]

Statistics Describing Spatial and Temporal Variability of Bottom Stress

Median: the value for which 50 percent of stress estimates fall below and 50 percent of stress estimates fall above 

(equivalent to the mean for a normal distribution)

Half interpercentile range: half of the difference between the 84th and 16th percentiles (equivalent to the standard 

deviation for a normal distribution)

95th percentile: the value exceeded by 5 percent of data in the time series (for example, 95 percent of output points are less 

than this value)

Statistics Describing Bed Mobility

Bed mobility percentage: percentage of time the critical stress threshold is exceeded at each location

Bed mobility recurrence interval: total number of mobility events divided by the total length of the time series, in days

Other statistics of the bottom stress and mobility time series may be developed and included in 

the database.

Data Format

Bottom stress and sea floor mobility statistics in the database are provided in ArcGIS shapefile 

format. Bottom stress statistics are provided in polygon format, with each polygon corresponding to a 

grid cell in the underlying numerical model. One shapefile is provided for each bottom stress statistic, 

with each file containing five attributes corresponding to the value calculated on the year and by season 

(winter, spring, summer, and fall). Sea floor mobility statistics are provided in point format, with each 

point corresponding to one sediment texture measurement.

Metadata

Fedeal Geographic Data Committee metadata are provided with each shapefile describing the 

underlying hydrodynamic and wave models, which vary by geographic region, used to generate the 

statistics contained within that file. The metadata include the types of numerical models used, the model 

spatial and temporal resolution, input data used, the time period over which output was calculated, and 

specific model parameters that would be necessary to recreate the results. The source of the sediment 

texture data used for generating critical stress values in the calculation of sea floor mobility is included 

with the sediment mobility files. Metadata also include any additional references, such as peer reviewed 

publications, reports, or Web sites that provide additional information on the models and their 

parameterizations. These metadata provide users with detailed information on the model and sediment 

parameters that will be helpful in interpreting the stress and mobility statistics.
6

Data Validation

Quality control (QC) checks are performed as part of model review, and errors are rectified 

before submission to the database manager for review prior to inclusion in the database.

Procedures for Quality Control.—The following protocols are used to ensure data quality:

• Model data are accessed from Web sites and other data servers in consultation with the principal 

investigators responsible for model operation to determine the most appropriate model output for 

stress characterization;

• In cases where model data are not available, the gaps are filled by selecting and implementing an 

appropriate model over the domain of interest;

• Wave and current model data are validated against field observations as available and 

appropriate;

• Data processing steps are documented and recorded;

• Stress and mobility statistics are examined for outliers or other artifacts; if found, the statistics 

and underlying stress time series are reviewed and corrected as necessary.

Data Review

The stress and mobility data are reviewed prior to inclusion in the database. After stress and 

mobility calculations are completed, files to be added to the database are reviewed by the database 

manager. This review verifies that

• metadata are complete and accurate; and 

• data format standards are met.

o Before inclusion in the database, statistics are also reviewed and interpreted by project 

scientists to verify that

• ranges, patterns, and trends are reasonable; and

• data and metadata formats are error-free.

Data are continually assessed as they are used in analysis by USGS and others. If errors or 

inconsistencies are discovered, then the data in the database are updated and changes documented in the 

metadata.

Database Access via the Web

A Sea Floor Stress and Sediment Mobility Database homepage 

(http://woodshole.er.usgs.gov/project-pages/mobility/) describes the database and the processes used to 

create it. The database is assembled by geographic regions of the U.S. Continental Shelf that 

approximately correspond to the U.S. Integrated Ocean Observing System (IOOS) regions 

(http://www.ioos.gov/). The Sea Floor Stress and Mobility data may be accessed through the USGS 

Internet map server (http://coastalmap.marine.usgs.gov/regional/contusa/index.html). Estimates of sea 

floor stress and mobility are being added to the online database as they are developed for each region.

Acknowledgments

Pat Dickhudt of Integrated Statistics provided recommendations on critical stress thresholds for 

cohesive beds.
7

Selected References

Churchill, J.H., Wirick, C.D., Flagg, C.N., and Pietrafesa, L.J., 1994, Sediment resuspension over the 

continental shelf east of the Delmarva Peninsula: Deep Sea Research Part II: Topical Studies in 

Oceanography, v. 41, nos. 2–3, p. 341–363.

Clauser, F.H., 1956, The turbulent boundary layer: Advances of Applied Mechachics, v. 4, p. 1–51.

Dickhudt, P.J., Friedrichs, C.T., and Sanford, L.P., 2011, Mud matrix solids fraction and bed erodibility 

in the York River estuary, USA, and other muddy environments: Continental Shelf Research, v. 31, 

no. 10, supplement, p. S3–S13.

Foreman, M.G.G., 1977, Manual for tidal heights analysis and prediction: Sidney, Canada, Institute of 

Ocean Sciences, Patricia Bay, Pacific Marine Science Report 77–10, 58 p.

Foreman, M.G.G., 1978, Manual for tidal currents analysis and prediction: Sidney, Canada, Institute of 

Ocean Sciences, Patricia Bay, Pacific Marine Science Report 78–6, 57 p.

Glenn, S.M., 1983, A continental shelf bottom boundary layer model—The effects of waves, currents, 

and a moveable bed: Cambridge, Mass., Massachusetts Institute of Technology and Woods Hole 

Oceanographic Institution Ph.D. dissertation, 237 p.

Glenn, S.M., and Grant, W.D., 1987, A suspended sediment stratification correction for combined wave 

and current flows: Journal of Geophysical Research, v. 92, no. C8, p. 8244–8264.

Godin, Gabriel, 1972, The analysis of tides: Toronto, Canada, University of Toronto Press.

Goud, M.R., 1987, Prediction of continental shelf sediment transport using a theoretical model of the 

wave-current boundary layer. Cambridge, Mass., Massachusetts Institute of Technology and Woods 

Hole Oceanographic Institution Ph.D. dissertation, 211 p.

Grant, W.D., and Madsen, O.S., 1979, Combined wave and current interaction with a rough bottom: 

Journal of Geophysical Research, v. 84, no. C4, p. 1797–1808.

Grant, W.D., and Madsen, O.S., 1982, Movable bed roughness in unsteady oscillatory flow: Journal of 

Geophysical Research, v. 87, no. C1, p. 469–481.

Grant, W.D., and Madsen, O.S., 1986, The continental-shelf bottom boundary-layer: Annual Review of 

Fluid Mechanics, c. 18, p. 265–305.

Hemer, M.A., 2006, The magnitude and frequency of combined flow bed shear stress as a measure of 

exposure on the Australian continental shelf: Continental Shelf Research, v. 26, no. 11, p. 1258–1280.

Holthuijsen, L.H., Booij, N., and Ris, R.C., 1993, A spectral wave model for the coastal zone, in

Magoon, O.T., and Hemsley, J.M., eds., Proceedings of the Second International Symposium on 

Ocean Wave Measurement and Analysis, New Orleans, La., July 25–28, 1993: New York, N.Y., 

American Society of Civil Engineers, p. 630–641.

Lyne, V.D., Butman, Bradford, and Grant, W.D., 1990a, Sediment movement along the U.S. east coast 

continental shelf—I. Estimates of bottom stress using the Grant-Madsen model and near-bottom wave 

and current measurements: Continental Shelf Research, v. 10, p. 397–428.

Lyne, V.D., Butman, Bradford, and Grant, W.D., 1990b, Sediment movement along the U.S. east coast 

continental shelf—II. Modelling suspended sediment concentration and transport rate during storms: 

Continental Shelf Research, v. 10, p. 429–460.

Madsen, O.S., 1994, Spectral wave-current bottom boundary layer flows: International Conference on 

Coastal Engineering, 24th, Kobe, Japan, Octobe 23–28, 1994, proceedings, p. 384–398.

Madsen, O.S., Poon, Ying-Keung, and Graber, H.C., 1988, Spectral wave attenuation by bottom 

friction–Theory: International Conference on Coastal Engineering, 21st, Coata del Sol-Malaga, Spain,

June 20–25, 1988, p. 492–504.
8

Madsen, O.S., Wright, L.D., Boon, J.D., and Chisholm, T.A., 1993, Wind stress, bed roughness and 

sediment suspension on the inner shelf during an extreme storm event: Continental Shelf Research, v. 

13, no. 11, p. 1303–1324.

Nikuradse, J., 1933, Strömungsgesetze in rauhen rohren [Laws of turbulent pipe flow in rough pipes]: 

VDI-Forchlungsheft 361. [Translated in National Advisory Commission for Aeronautics, Technical 

Memorandum 1292, 1950.]

Panagiotopoulos, I., Voulgaris, G., and Collins, M.B., 1997, The influence of clay on the threshold of 

movement of fine sandy beds: Coastal Engineering, v. 32, no. 1, p. 19–43.

Pawlowicz, Rich, Beardsley, Bob, and Lentz, Steve, 2002, Classical tidal harmonic analysis including 

error estimates in MATLAB using T_TIDE: Computers & Geosciences, v. 28, p. 929–937.

Sanford, T.B., and Lien, Ren-Chieh, 1999, Turbulent properties in a homogeneous tidal bottom 

boundary layer: Journal of Geophysical Research, v. 104, p. 1245–1257.

Shchepetkin, A.F., and McWilliams, J.C., 2005, The regional oceanic modeling system (ROMS)—A 

split-explicit, free-surface, topography-following-coordinate oceanic model: Ocean Modelling, v. 9, 

no. 4, p. 347–404.

Soulsby, Richard, 1997, Dynamics of marine sands—A manual for practical applications: London, 

Thomas Telford Publications, p.

Torfs, H., Jiang, J., and Mehta, A.J., 2000, Assessment of the erodibility of fine/coarse sediment 

mixtures: Proceedings in Marine Science, v. 3, p. 109–123.

van Ledden, M., van Kesteren, W.G.M., and Winterwerp, J.C., 2004, A conceptual framework for the 

erosion behaviour of sand-mud mixtures: Continental Shelf Research, v. 24, no. 1, p. 1–11.

Welch, P.D., 1967, The use of fast fourier transform for the estimation of power spectra—A method 

based on time averaging over short, modified periodograms: IEEE Transactions on Audio and 

Electroacoustics, v. 15, p. 70–73.

Zhenlin Li, Michael, 1994, Direct skin friction measurements and stress partitioning over movable sand 

ripples: Journal of Geophysical Research, v. 99, no. C1, p. 791–799.
9

Glossary

δw Thickness of the wave bottom boundary layer (measured in meters)

τcr Critical stress threshold (measured in pascals)

τcurr Current-induced bottom shear stress (measured in pascals)

τwave Wave-induced bottom shear stress (measured in pascals)

τwc Combined wave- and current-induced bottom shear stress (measured in pascals)

d50 Median grain size (measured in meters)

kb Bottom roughness defined as Nikuradse sand grain size (measured in meters)

Tbr Representative bottom wave period (measured in seconds)

ubr Representative bottom orbital velocity (measured in meters per second)

WBL Wave bottom boundary layer (measured in meters)

zR Current reference height (measured in meters)
For more information concerning this report, contact

Director

U.S. Geological Survey

Woods Hole Coastal and Marine Science Center

384 Woods Hole Road

Quissett Campus

Woods Hole, MA 02543-1598

WHSC_science_director@usgs.gov

508-548-8700 or 508-457-2200

or visit our Web site at

http://woodshole.er.usgs.gov
Dalyander and others— Documentation of the U.S. Geological Survey Sea Floor Stress and Sediment Mobility Database—Open-File Report 2012-1137