Mitigation Through Surf Enhancement/Appendix A

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Mitigation Through Surf Enhancement
An Early History of Pratte's Reef
HomeAcknowledgementsAbstractIntroductionChapter 1Chapter 2Chapter 3ConclusionsAppendix AAppendix BBibliography
Note Note: This paper documents the background and theory behind an Artificial Surfing Reef (ASR) that was constructed in El Segundo, CA in 2000. Evaluation of the effects of this reef determined that it did not improve surfing conditions and has led to its removal, with phase one of the removal process beginning in 2008. For more information, see the article Pratte's Reef

Modeling Ocean Gravity Waves with REF/DIF 1

REF/DIF 1 represents a new breed of ocean wave models that have a number of strengths over traditional modeling methods. It is important to remember that REF/DIF is a model with limitations and assumptions that may divorce model results from actual wave responses. These strengths and weaknesses are discussed below. Included is a section on program input particular to the modeling efforts of this study. REF/DIF is capable of modeling many situations that are more involved than those presented here. The interested reader should consult the users manual (Kirby and Dalrymple, 1994) for additional information about REF/DIF 1.


REF/DIF 1 is a weakly non-linear combined refraction and diffraction model which incorporates the shoaling, refraction, energy dissipation and diffraction of propagating waters waves. REF/DIF 1 models wave heights and directions on a model grid rather than on irregularly spaced rays, this is a major strength because it avoids the difficulties associated waving ray crossing that may lead to uninterpretable results (Kirby and Dalrymple, 1994). Traditionally models had to suspend refraction in areas were diffraction is dominant. Far from the diffraction area, refraction is resumed. Although this technique allows inclusion of diffraction in an approximate way, it is clearly an inaccurate method. REF/DIF 1 combines both refraction and diffraction explicitly, thus permitting the modeling of waves in regions where the bathymetry is irregular and where diffraction is important (Kirby and Dalrymple, 1994).


REF/DIF 1 propagates monochromatic waves across the bathymetry grid. Because waves in most natural situations are Rayleigh distributed in height and frequency and also have a complex directional component, it is important to recognize that REF/DIF 1 results presented in this study are based on a single wave with a specific height and frequency. In addition REF/DIF propagates waves in one direction per run. The model, in parabolic form, ignores reflection. This may be an important omission when investigating an artificial reef with a steep toe angle such as the reefs modeled in this study.

The REF/DIF 1 model, in parabolic form, has a number of assumptions:

  1. Mild Bottom Slope. The mathematical derivation of the model assumes that the variations of the bottom occur over distances which are long in comparison to a wave length. It was found that for bottom slopes up to 1:3 the mild slope model was accurate and for steeper slopes it still predicted the trends of wave height changes correctly. The reef bathymetries are in violation of the mild bottom slope (Kirby and Dalrymple, 1994). A toe angle of 80° has a bottom slope of over 1:0.17 (significantly steeper than 1:3). It is unknown how this violation affects the model results.
  2. Weak nonlinearity. Strictly the model is based on a Stokes perturbation expansion and therefore is restricted to applications where Stokes waves are valid, unless the Stokes-Hedges nonlinear model dispersion relationship is selected. In this case, a heuristic dispersion relationship developed by Hedges (1976) is used. In shallow water this relationship matches that of a solitary waves. This hybrid model is discussed in more detail in Kirby and Dalrymple (1986). In this study the Stokes-Hedges dispersion relationship is always turned on because the waves are propagating over a shallow reef (discussed below).
  3. The wave direction is confined to a sector ±70° to the principal assumed wave direction. This did not present a limitation to this study because no wave direction that lead to an angle larger than 40° was considered.

Program Input: Model Control and Wave Data

In order to operate the REF/DIF 1 on a bathymetry grid several files must be created. A file called param.h must be created which is used to store the dimension of the grid. The grid sized used in this study was 200 by 200 cells for all model runs. Next a file must be created that includes information about the bathymetry grid and the wave climate for each run. Once the program called datgen25.f is edited for the appropriate grid size (the file contains code specific to the grid size), compiled and run, this data is easily input for each model run via the executable form of datgen25.f. The file that is generated is called indat.dat. The example below is the input instructions and inputs for a typical model run from the datgen25.f executable. The bold text are the instructions and the italic text are the users input responses.

enter name for .dat file containing reference grid in' single quotes
enter name for output data file
enter grid dimensions mr, nr
enter grid spacings dxr, dyr and depth tolerance dt
input iu: 1=mks, 2=english
input dispersion relationship; ntype: 0=linear,
1=composite, 2=stokes
input lateral boundary condition; ibc: 0=closed
input ispace (0=program picks x spacing, 1=user chooses)
input nd (# y divisions, 1 is minimum)
input if(1) turbulent, if(2) porous, if(3) laminar
standard choice: 1, 0, 0
input isp (subgrid features) :standard 0
input values of iinput, ioutput:
iinput: 1 standard, i.e., not starting from previous run
2 if starting from previous run
ioutput: 1 standard, not saving restart data
2 if saving restart data
input value of isurface:
isurface = 0: no surface picture generated
isurface = 1: surface picture generated
input iwave (1 discrete, 2 directional spread)
input nfreq (# of frequencies)
input wave period and tide stage
input # of waves per frequency, nwavs
input amplitude and direction

The first input is the name of the ASCII version of bathymetry array which must be entered in single quotes.

The second input in the name of the output file. This file is always called output.dat and also single quoted.

The grid dimensions mr and nr are the sides of your bathymetry grid which was 200 by 200 for all grids used in this study.

The grid spacings dxr and dyr control the scale of your grid. Each grid cell in this study was 5 meters by 5 meters. The depth tolerance dt is a tolerance for steps in the bathymetry grid. Any vertical step larger than the tolerance reports an error. In this study all bathymetries had a step no larger than one, therefore 5 was used for convenience.

The input iu: controls the units of the grids spacing. The metric system was used for this modeling.

The dispersion relationship ntype selects the model option that is used for shallow water wave propagation. In this study the composite relationship, which is a Stokes-Hedges model (See Assumptions above), was always used because the wave propagated over shallow reef structures.

The lateral boundary condition ibc was always open for this study. This creates "reasonably transparent" boundaries on the edges of the grid. It is suggested that the boundary condition is tested with the closed option to determine the potential amount of interference by waves "reflecting" off the lateral boundaries (Kirby and Dalrymple, 1994). In this study the model was run with the boundary condition closed with no noticeable effects.

The input ispace and input nd control the number of subdivisions used by the model to iterate through the grid. The input ispace was always set to 0 allowing the program to pick the x spacing. It is important that there are at least 5 subdivisions in the y direction per wavelength for the model to operate correctly (Kirby and Dalrymple, 1994). In this study this was determined that 1 division still allowed for at least 5 subdivisions per wavelength for a 12 second wave.

In the input iff controls the dissipation from three boundary layers: the turbulent boundary layer, bottom damping and laminar boundary layers. Because dissipation was not a concern in this study all boundary layer dissipations were turn off (set to zero). This suggests that wave heights after breaking are maximized for all cases.

The subgrid features input isp allows a subgrid to be entered in the bathymetry grid with a finer resolution. Subgrids were not used in this study (isp = 0).

The inputs iinput and ioutput allow for data for a separate model run to be incorporated into the current modeling run. Because all model runs were conducted in their entirety iinput and ioutput were always turned off (set to 1).

Surface plots of propagated waves can be generated by setting isurface to 1. This was not typically done, however some surface plots were investigated.

The input iwave controls the wave field type: discrete waves or a directional spreading model. In this study all models were run with a discrete wave (iwave = 1) with one frequency (nfreq = 1). The wave period controls the period of the propagating wave. Wave period is entered in seconds. A wave period of 12 seconds was determined to be the average period in El Segundo in surfable conditions. The tide stage input controls the water level on the bathymetry by either adding or subtracting the number of units input as tide stages. For example a tide stage of -2 would subtract two meters from the depths of the bathymetry. This was not used in this study. Instead the bathymetry was altered to represent different depths.

The input nwavs controls the number of waves per frequency. This was always set to 1 wave. The input amplitude is the wave amplitude at the first set of offshore grid cells. It is important to remember that amplitude is one half the wave height (H). The direction controls the propagation direction relative the to the x-axis. This was usually set to zero.

Once the model is run several ASCII files are generated with a resolution equal to that of the input bathymetry grid. The time it takes per model run is dependent on the grid size and computer speed. Some large grids can take up to an hour to run, the average run time for this study was approximately 3 minutes. The output files include height.dat, depth.dat, angle.dat which are discussed in Chapter 3. In addition several radiation stress files are created. These output files were not investigated in this study.