Half interpercentile range (half of the difference between the 16th and 84th percentiles) of wave-current bottom shear stress in the Middle Atlantic Bight for May, 2010 - May, 2011 (MAB_hIPR.SHP)

The Simulating WAves Nearshore (SWAN) numerical wave model (version 40.81, modified for proper calculation of RMS bottom orbital velocity and for output of bottom wave direction) was used to create a time-series of bottom orbital velocity, bottom representative period, and bottom wave direction over the one year time period of May, 2010 - May, 2011 in each grid cell in the model domain. The wave model SWAN 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. Although stress calculations were only performed over the spatial extent of the hydrodynamic model, SWAN was run over a larger spatial scale. This ~5 km resolution grid, which covers the U.S. East Coast, Gulf of Mexico, and much of the western north Atlantic, was originally developed for use with the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) model system forecast and is shown elsewhere (Warner et al., 2010). This domain pushes the boundaries of the grid far from the region of interest to allow the wave spectrum (relatively important in calculations of stress) to evolve away from the boundary. The model was run for April 2010 using the default SWAN initial condition formulation for a non-stationary run, e.g., a JONSWAP spectrum from prescribed initial wind conditions, to develop initial conditions for the one year study period (May 2010 to May 2011). Significant wave height, dominant wave period, and wave direction were prescribed as SWAN TPAR format files on the model grid boundary with a spatial resolution of a boundary point every 25 grid cells using results from the NOAA Wavewatch III global multi-grid model, updated every 3 hours. A JONSWAP (JOint NOrth Sea WAve Project) spectral shape was assumed at these boundary points. Wind forcing was provided at 3-hour resolution from the NOAA North American Mesoscale (NAM) model (12 km resolution) over its domain, with forcing at the most offshore portions of the grid (outside the NAM grid) provided by the NOAA Global Forecasting System (GFS) model at 0.5 degree resolution. The SWAN directional resolution was 6 degrees (60 bins), determined via sensitivity analysis as the coarsest (and hence least computationally expensive) resolution that does not result in the "Garden-Sprinkler Effect" (GSE), wherein swell traveling over large distances inaccurately disintegrates into non-continuous wave fields as a result of frequency and directional discretization. The minimum frequency bin should be set to a value less than 0.7 times the lowest expected peak frequency and the maximum frequency bin should be set at least 2.5-3 times the highest expected peak frequency expected. In order to determine appropriate values, the peak periods from 43 NDBC buoys throughout the wave model domain were analyzed (when available) over the one year period of the study, yielding 297,533 hourly observations. The 99th and 1st percentiles of peak period were 15 s and 3 s, corresponding to frequencies of 0.07 Hz and 0.33 Hz, noting that these values may be biased by buoy limits of detection at high and low frequencies. The frequency range was therefore specified as 0.04-1 Hz. SWAN was allowed to internally determine the frequency resolution as one tenth of each frequency bin for best performance of the discrete interaction approximation (DIA) method of nonlinear 4-wave interactions, resulting in 34 frequency bins. Bottom friction calculations used the Madsen formulation with a uniform roughness length scale of 0.05 m. This value was selected for the best comparison of model output and buoy observations within the domain, and does not correspond to physical roughness values or the bottom roughness used in stress calculations. Wind generation and whitecapping parameterizations follow the modified Komen approach prescribed by Rogers et al. (2003), which reduces inaccurate attenuation of swell energy by whitecapping. Wave model outputs of bottom orbital velocity, bottom representative period, and bottom wave direction were output hourly and interpolated onto the ESPreSSO model grid. NDBC observations were used for model validation; ten full-spectra wave buoys are within the domain. Due to maintenance problems observations from all buoys were not available over the entire time period and data from Texas Tower Station 44066 for January 2011, when the buoy was adrift but still reporting, were manually removed. Using the GM method and the same bottom roughness of 0.005 m used to process model output, surface and bottom parameters were calculated from buoy spectra and compared to model output at the same locations. The same person that conducted this processing step conducted each subsequent processing step. References: Rogers, W.E., Hwang, P.A., Wang, D.W., 2003. Investigation of Wave Growth and Decay in the SWAN Model: Three Regional-Scale Applications. J. Phys. Oceanogr. 33, 366-389. Warner, J.C., Armstrong, B., He, R., Zambon, J.B., 2010. Development of a Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) Modeling System. Ocean Modelling 35, 230-244.

Use the wave model and current model results to calculate the time series of bottom shear stress within each model grid cell using Mathworks MATLAB software (v2011A). Bottom shear stress estimates are made following Grant-Madsen (GM) (Madsen, 1994), from the estimated bottom orbital velocities and bottom wave periods generated with SWAN, and near-bed current estimates from the ESPreSSO hydrodynamic model. The GM approach relies on an eddy viscosity turbulence closure model and formulates the wave stress, current stress, and combined wave-current bottom stress as functions of a representative bottom wave orbital velocity, representative bottom wave period, current flow at some reference height, the angle between wave and current propagation, and bottom roughness. Full details of the GM formulation may be found elsewhere (Glenn, 1983; Glenn and Grant, 1987; Grant and Madsen, 1979, 1982, 1986; Madsen, 1994; Madsen et al., 1988). 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 taken as the distance from the cell vertical midpoint to the seabed. GM 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 calculated using GM exceeds of one or more of the deepest grid cells, the current estimate and associated reference height are used from the deepest grid cell at each location where the reference height exceeds the width of the WBL. 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% 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 magnitude 10's of meters (Goud, 1987), a maximum value for reference height is set as 5 m. 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. References: Madsen, O.S., 1994. Spectral wave-current bottom boundary layer flows, Proceedings 24th Conf. Coastal Eng., pp. 384-398. Glenn, S.M., 1983. A Continental Shelf Bottom Boundary Layer Model: The Effects of Waves, Currents, and a Moveable Bed. Dissertation, Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, Cambridge, MA, 237 pp. Glenn, S.M., Grant, W.D., 1987. A suspended sediment stratification correction for combined wave and current flows. J. Geophys. Res. 92, 8244-8264. Goud, M.R., 1987. Prediction of Continental Shelf Sediment Transport Using a Theoretical Model of the Wave-Current Boundary Layer. Dissertation, Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, Cambridge, MA, 211 pp. Grant, W.D., Madsen, O.S., 1986. The continental-shelf bottom boundary-layer. Annu. Rev. Fluid Mech. 18, 265-305. Grant, W.D., Madsen, O.S., 1982. Movable bed roughness in unsteady oscillatory flow. J. Geophys. Res. 87, 469-481. Grant, W.D., Madsen, O.S., 1979. Combined wave and current interaction with a rough bottom J. Geophys. Res. 84, 1797-1808. Madsen, O.S., 1994. Spectral wave-current bottom boundary layer flows, Proceedings 24th Conf. Coastal Eng., pp. 384-398. Madsen, O.S., Poon, Y., Graber, H.C., 1988. Spectral wave attenuation by bottom friction: theory, Proceedings 21st Int. Conf. Coast. Eng., pp. 492-504.

Calculate the half interpercentile range of bottom shear stress by year and season in Mathworks MATLAB software (v2011A). This value is calculated as half of the difference between the 16th and 84th percentiles of the time series within each grid cell, and would be equal to the standard deviation of the the observations followed a normal distribution. These statistical values are saved in MATLAB .mat format.

Export the values for each grid cell from MATLAB format into an ArcGIS shapefile using the Mathworks MATLAB Mapping Toolbox (v2011A). Grid cells where the height of the deepest grid cell in the circulation model is always above the maximum accepted reference height for validity of a log-profile assumption (necessary for stress calculations) are excluded and not exported to Arc. In some cases, data may exist during parts of the year and not others; in this case, the statistic is calculated and included for the season where model output exist, and a missing data value of -9999 (replacing the MATLAB native NaN format) is used for seasons where no valid statistic can be calculated. A geographic data structure is created in MATLAB with the following fields: Geometry ('Polygon'), Lon (the five longitude points defining each grid cell, with one of the four grid corner values repeated to close the polygon in Arc), Lat (same as Lon, for the latitude points of the grid), Year (the statistic calculated for the entire year), Winter (the statistic calculated for December, January, and February), Spring (the statistic calculated for March, April, and May), Summer (the statistic calculated for June, July, and August), and Fall (the statistic calculated for September, October, and November). The shapefile is then 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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