Hydrodynamic and Sediment Transport Model Application for OSAT3 Guidance: Ratio of the wave- and current-induced shear stress to the critical value for oil-tar balls and sediment mobilization weighted by probability of wave scenario occurrence

Using observed wave conditions from NOAA buoy 42040 and Mathworks MATLAB software 2012A, the hourly wave buoy observations between 04/01/2010 and 08/01/2012 were each classified as falling into 1 of 80 wave scenarios defined by wave height and direction. For each scenario, a specific time step was identified in the record which was most representative of the other observations within the same wave height and direction bins based on both wave (height, period, and direction) and wind (speed and direction) characteristics. The characteristics of these scenarios, along with the percentage of observation in the record and the chosen representative time period, may be found in wave_scenarios.txt. The probability of occurrence for each wave scenario along with its characteristics and representative time periods were saved in MATLAB .mat format.

The D-Flow and D-Waves components of the Deltares Delft3D numerical model suite (version 4.00.01) were used to estimate bottom orbital velocity, peak period, peak wave direction, and east and north components of wind and wave-driven velocity for the offshore wave conditions corresponding to each scenario's representative time period (characteristics of which may be found in the included wave_scenarios.txt file) in each grid cell in the model domain. The wave model D-Waves, based on the Simulating WAves Nearshore (SWAN) model, is a 3rd generation phase-averaged numerical wave model which conserves wave energy subject to generation, dissipation, and transformation processes and resolves spectral energy density over a range of user-specified frequencies and directions. D-Wave was used in stationary mode. D-Flow solves the shallow water Navier Stokes equations and is run in 2-D depth-averaged mode, with linkage to D-Waves allowing the generation of wave-driven currents via wave radiation stress forcing. Default values for model parameters governing horizontal viscosity, bottom roughness, and wind drag were used. Neumann boundary conditions were used along the east, west, and south model boundaries with harmonic forcing set to zero. Model bathymetry was provided by the NOAA National Geophysical Data Center Northern Gulf Coast digital elevation map, referenced to NAVD88.
Significant wave height, dominant wave period, and wave direction were prescribed as D-Wave TPAR format files every 30 grid cells along the model boundary using results from the NOAA Wavewatch III 4' multi-grid model for a representative moment in time corresponding to the offshore wave conditions of the scenario, the specific time of which may be found in the included wave_scenarios.txt file. A JONSWAP (JOint NOrth Sea WAve Project) spectral shape was assumed at these boundary points. Wind forcing was provided using the archived WavewatchIII 4' winds, extracted from the NOAA GFS wind model, for this time. The D-Wave directional space covers a full circle with a resolution was 5 degrees (72 bins). The frequency range was specified as 0.05-1 Hz with logarithmic spacing. Bottom friction calculations used the JONSWAP formulation with a uniform roughness coefficient of 0.067 m2/s3. 3rd-generation physics are activated which accounts for wind wave generation, triad wave interactions and whitecapping (via the Komen et al parameterization). Depth-induced wave breaking dissipation is included using the method of Battjes and Janssen with default values for alpha (1) and gamma (0.73). Wave model outputs of bottom orbital velocity, peak period, and peak wave direction were extracted on the wave model grid, and current model outputs of east and north current velocity component were extracted and interpolated to the wave model grid (staggered points in relation to the current model grid).
NDBC observations from station 42012 for the representative scenario time periods were used to validate the wave model results.

Use the wave model and current model results to calculate the bottom shear stress within each model grid cell for each scenario using Mathworks MATLAB software (v2012A). The wave-current stress was calculating following the method of Soulsby (1995) to parameterize four methods giving good overall performance for estimating wave-current stress, based on original formulations by Grant and Madsen (1979), Fredsøe (1984), Huynh-Thanh and Temperville (1991), and Davies et al. (1998). The combined wave-current stress for the individual components of wave and current stress was calculated for hydrodynamic model output following the method prescribed in Soulsby (1997) for each of the four methods. The mean value of the four methodologies was used to estimate the combined wave-current shear stress for each hydrodynamic scenario. Wave direction, bottom orbital velocity, and period, and depth-averaged current magnitude and direction, required for this calculation, are calculated internally by the model. The roughness used is 1/12 the diameter of the SRB or sediment being analyzed, following Soulsby (1997). Stress values are saved in MATLAB .mat format.
The same individual who completed this processing step completed all additional processing steps.
References: Davies, A.G., Soulsby, R.L., King, H.L. (1988). A numerical model of the combined wave and current bottom boundary layer. J. Geophys. Res. 93, 491-508.
Fredsøe, J. (1984). Turbulent boundary layer in wave-current motion. J. Hydraul. Eng. ASCE (110), 1103-1120.
Grant, W.D., Madsen, O.S. (1979). Combined wave and current interaction with a rough bottom. J. Geophys. Res. (84), 1797-1808.
Huynh-Thanh, S., Temperville, A. (1991). A numerical model of the rough turbulent boundary layer in combined wave and current interaction, in Sand Transport in Rivers, Estuaries, and the Sea, eds. R. L. Soulsby and R. Bettess, pp 93-100. Balkema, Rotterdam.
Soulsby, R.L. (1995). Bed shear-stresses due to combined waves and currents, in Advances in Coastal Morphodynamics, eds. M.J.F. Stive, H.J. de Vriend, J. Fredsøe, L. Hamm, R.L. Soulsby, C. Teisson and J.C. Winterwerp, pp. 4-20 and 3-23. Delft Hydraulics, Netherlands.
Soulsby, R.L. (1997). Dynamics of Marine Sands. Thomas Telford Publications: London, 249 pp.

Estimate the critical shear stress for 300 micron quartz sediment and 6 SRB size classes and take the ratio of the combined wave-current stress to this critical value at each grid point for each scenario. The specific characteristics for the sediment and SRB classes may be found in the included SRB_classes.txt file. Calculations are performed in Mathworks MATLAB (v2012A). Critical stress thresholds are calculated using the Shield's parameter following Soulsby (1997) and saved in MATLAB .mat format. These ratios may also be found in ArcGIS format within the same OFR containing this layer, with naming convention Hh_Dd_mobility corresponding to results for scenario Hh_Dd. In the case of SRBs, the Shield's parameter is identified as a "high" critical stress value, corresponding to instances when an SRB of the identified size is within a uniform bed of similarly sized SRBs. Exposure above the bed, such as may occur with a single SRB on a sand band, reduces the critical shear stress value for incipient motion. Based on field observations of gravel and sand mixtures, a "medium" critical stress value is calculated from a constant non-dimensional Shields parameter of 0.02, and a "low" critical stress value is calculated from a constant non-dimensional Shields parameter of 0.01 (Andrews, 1983; Bottacin-Busolin et al, 2008; Fenton and Abbott, 1977; Wiberg and Smith, 1987; Wilcock, 1998). Because the in-situ sediment is assumed to be of a relatively uniform size, a single critical stress value based on the Shields parameter is used.
References:
Andrews, E.D. (1983). Entrainment of gravel from naturally sorted riverbed material. Geo. Soc. Amer. Bull. (94), 1225-1231.
Bottacin-Busolin, A., Tait, S.J., Marion, A., Chegini, A., Tregnaghi, M. (2008). Probabilistic description of grain resistance from simultaneous flow field and grain motion measurements. Water Resources Res. (44), WO9419.
Fenton, J.D., Abbott, J.E. (1977). Initial movement of grains on a stream bed: the effect of relative protusion. Proc. R. Soc. Lond. A. (352), 523-537.
Soulsby, R., 1997. Dynamics of Marine Sands, a Manual for Practical Applications. Thomas Telford Publications, London.
Wibert, P.L., Smith, J.D. (1987). Calculations of the Critical Shear Stress for Motion of Uniform and Heterogenous Sediments. Water Resources Res. (23), 1471-1480.
Wilcock, P.R. (1998). Two-Fraction Model of Initial Sediment Motion in Gravel-Bed Rivers. Science (280), 410-412.

For each scenario, the ratio of stress to critical stress for sediment and each SRB class was converted into a binary matrix of zeros and ones, with zero at all location where the ratio was less than 1 (indicating no mobility) and one at all locations where the ratio was greater than 1 (indicating mobility). The average of this value in each grid cell for sediment and each size of SRB was calculated for each scenario, weighting the scenario value by the percent observation of that scenario in the time period of 04/01/2010 to 08/01/2012.

Exported the values for each grid cell from MATLAB format into an ArcGIS shapefile using the Mathworks MATLAB Mapping Toolbox (v2012A). Land grid cells are not exported to Arc. The shapefile is written with the "shapewrite" command. Because MATLAB does not assign a projection, the projection corresponding to the projection associated with the bathymetry used in the numerical models is added in ArcCatalog 9.3. The file was then quality checked in ArcMap to insure values were properly exported to the shapefile from MATLAB.

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