Mitigation Through Surf Enhancement/Chapter 3
From Beachapedia
| Mitigation Through Surf Enhancement An Early History of Pratte's Reef | |||||||||||
|
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 ReefModeling Wave Transformation Over An Artificial Reef
Introduction
Now that a collaborative effort between Surfrider Foundation, Chevron, and the California Coastal Commission has been established to enhance the surf near El Segundo the task at hand is to create an artificial surfing reef that creates a "ridable" wave. Although there have been extensive studies on the effects of submerged breakwaters both on the transformation of wave energy and on shoreface response (Kobayashi and Wurjanto, 1989, Grilli, et al., 1994, Dalrymple and Martin, 1990, and Hsu, 1990) no such structure has been created specifically to enhance recreational surfing. In order to examine the important reef characteristics involved in creating a "surfable" wave at the El Segundo sight before the actual reef is constructed, I employed a computer model of wave refraction and diffraction to simulate waves breaking on a reef-enhanced shoreline. Using Kirby and Dalrymple's (1994) REF/DIF1 wave model, simulated waves were propagated cross-shore over bathymetries that included a reef design on a planar beach characteristic of the El Segundo area. By manipulating the reef shape and location and examining the wave response, the model predictions can be examined to identify important reef design characteristics.
Waves and Wave Modeling
REF/DIF1 is representative of a new group of water wave models that have significantly improved accuracy in comparison to previous models. Until recently, only very approximate models existed which relied on ray tracing techniques and excluded diffraction. These models had difficulties modeling waves propagation over complex bathymetries. REF/DIF1 is a weakly non-linear combined refraction and diffraction model that models waves on a uniform grid, thus avoiding many of the shortcomings in ray tracing techniques (Kirby and Dalrymple, 1994). Some explanation of wave propagation and transformation as waves approach the shore will clarify the modeling procedure.
Most ocean waves are generated by winds offshore. The size of the waves is dependent on three factors: wind speed, the duration of the wind, and the fetch or distance over which the wind blows (Denny, 1988). As this wind-generated chaotic sea moves away from the source their character changes. The waves organize into swells and tend to propagate in groups and their shape becomes sinusoidal. Because of the relatively simple shape and behavior of these waves traveling in very deep water, they can be described by what is known as linear wave theory, a simple water wave description. Linear wave theory has a number of assumptions, the most important for the modeling application discussed here is that linear wave theory assumes that wave height is infinitesimal relative to water depth (Denny, 1988).
As waves approach the shoreline and shoal (interact with the ocean floor) they transform dramatically in several ways. Waves can be refracted, reflected, diffracted, and they can break. Diffraction occurs as waves pass a structure (i.e. island or a jetty) and energy is propagated around the structure causing the wave to "wrap" around the structure. This "wrap around" effect is responsible for many great surfing areas located near headlands where the waves "wrap around" the headland into the shadowed area and form clean, surfable waves [See Figure 3.1].
A simple example of refraction occurs when obliquely approaching waves encounter a straight coast with parallel contours, the inshore part of each wave crest is slowed compared to the offshore part of the wave front as wave speed is roughly dependent on depth.
(where C is wave speed, g is the acceleration of gravity, and h is water depth)The result is that the offshore part of the wave front swings forward relative to the slowing part and the wave crests tend to align with the coastal contours (Bascom, 1980) [See Figure 3.2]. On an irregular coast wave crests tend to converge at the headlands and concentrate wave energy.
Conversely, wave crests tend to diverge in bays and coves resulting in a reduction of wave energy [See Figure 3.3]. Refraction can be an important factor in creating "peaky" waves in the surfing in areas with broad flat sand bars. The sand bars acts as a submerged micro-headland that acts to focus wave energy at the reef site. The refractive response of the waves to the sandbar will focus wave energy creating a peak in the wave crest, this can result in a wave that is suitable for surfing.
As shoaling waves approach the shore, wave celerity (speed) slows, the wavelength decreases, and wave height increases. Once waves begin shoaling the infinitesimal height assumption of linear theory is often broken. In addition, the wave is steepened in such a way that linear wave theory can not accurately describe the wave. Guza and Thorton (1980) demonstrated that although these violations to linear wave theory occur, linear theory still does an adequate job ( ± 20%) of describing many of the behaviors of breaking waves. Linear theory implies that all formulas governing wave behavior are first order (no variables are raised to a power higher than 1). Non-linear theory implies that equations that are to an order greater than one are applied to wave description. By way of analogy, first order equations always describe straight lines, whereas, higher order equations describe lines with increased curvature for every increase in power. Efforts to more accurately describe waves have applied non-linear theory to the description of waves. Using complex Boussinesq equations, non-linear wave theory relaxed the infinitesimal wave height assumption and allowed for wave harmonics to interact. These new models more accurately describe shoaling waves and contain information about wave motion that is necessary to explain wave driven sediment movement. However, these models still do not accurately predict wave motions once breaking occurs (Freilich and Guza, 1984). REF/DIF 1 applies weakly non-linear theory to simulate propagating waves. Weakly non-linear theory as applied by REF/DIF 1 is based on a Stokes expansion of the water wave problem and includes the third order correction to the wave phase speed. The wave height is known to the second order (Kirby and Dalrymple, 1994). This means that REF/DIF 1 uses second and third order equations to describe wave behavior more accurately than linear theory. A more detailed explanation of the strengths, weaknesses and operation of REF/DIF 1 is described in Appendix A.
Thorton and Guza (1982) found that waves become "energy saturated" in the inner surf zone demonstrated by a strong wave height dependence on water depth. This criteria requires wave breaking when wave height equals 0.78 of the water depth or y = H / h = 0.78 where y is wave break criteria, H is the significant wave height, and h is water depth (Thorton and Guza, 1982). It is this criteria that REF/DIF 1 applies to determine where breaking occurs. As waves approach a beach, eventually they will reach this saturation point and break. Investigation of this gamma value and empirical evidence suggests that waves will break farther offshore when the beach has a lower slope because the critical 0.78 ratio will occur farther out at sea. On beaches with a steep shoreface the wave will break closer to the beach. On an "over-steepened" beach, such as El Segundo, the breaking point can been moved farther offshore by the installation of an artificial reef [See Figure 3.4].
Methods
Modeling wave transformation over the surfing reefs required the input of a bathymetry grid, specification of initial wave conditions, and generation of model results using REF/DIF1. The bathymetry grids were generated in Matlab. The grid was 200 cells on each side. Each cell represented 5 meters on a side for a total represented area of 1 square kilometer. The baseline slope of the entire grid was 0.03. This was determined to be representative of the nearshore environment in El Segundo using the 1:40,000 scale Santa Monica Bay NOAA map [Chart# 18744]. At the kilometer scale the beach in El Segundo is primarily planar. On this planar shoreface the surfing reef was superimposed to create the model grid. The surfing reef is a V-shaped solid [See Figure 3.5] which is approximately 50 meters on a side and ranges from 3 - 6 meters in height. The reef is located in the center of the grid in the longshore direction and varies from 100 meters to 200 meters offshore. The distance offshore, toe angle, reef height, and nose angle are all variable parameters that can be changed each time a bathymetry is generated.
The necessary parameters required by REF/DIF 1 to propagate waves over a bathymetry grid are the wave amplitude (1/2 the wave height ) at the farthest offshore row of grid cells, the wave period, and the wave direction. In order to accurately model waves in the El Segundo area the wave climate was determined and input into the model. Because surfable waves do not occur in a regular or predictable manner, it was determined that waves with a 1.5 meter height represented an average surfable wave (Noble, 1992). The average period of the waves approaching El Segundo was determined to be 12 seconds (O'Reilly and Guza, 1993, & personal communication). Examination of O'Reilly's Spectral Model of Southern California (O'Reilly and Guza, 1993) and results from the Noble (1990) report indicated that the majority of waves approaching El Segundo are nearly shore normal because shadowing and refraction due to the Channel Islands. The Channel Islands are found offshore to both the north and the south of El Segundo [See Figure 3.6].
With the "typical surfing conditions" established and the reef bathymetries created, the next step was to run the REF/DIF 1 [See Appendix A for a discussion on REF/DIF 1 operations]. Once the wave climate conditions and the bathymetry are input into REF/DIF and the model is run, REF/DIF outputs three files important to this project: wave height, depth, and break point. The wave height file is used as a visual check to see that the model ran correctly and contains the wave response, as expressed in height, to the shore and the reef. My model results are analogous a test of the model performed by Kirby and Dalrymple (1994), therefore as a visual check, I expected my results to have a similar pattern. The depth file is used as a check to ensure that the bathymetry was correctly input into the model. The wave breaking file consisted of a line that indicated where the model broke the wave. This file is also used to observe wave response to the reef. Over thirty model simulations were run in an effort to test the model, investigate whether the model would simulate wave breaking over a reef, and to explore reef characteristics that would enhance surfing and create a surfable wave in El Segundo. Each parameter was tested independently. The specific results are considered in more detail below [See tables 1-4].
Table 1
1
|
0.03
|
0.053
|
0.3006
| ||||||
2
|
0.03
|
0.094
|
0.2256
| ||||||
3
|
0.03
|
0.131
|
0.1909
| ||||||
4
|
0.03
|
0.049
|
0.3117
| ||||||
Table 2
Table 3
| Direction | |||
| (degrees) | |||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
0
|
|||
5
|
|||
10
|
|||
15
|
|||
30
|
|||
Table 4
Results
For each set of reef parameters (nose angle, reef height or depth, toe angle, and offshore distance) and REF/DIF parameters (period, amplitude, and direction) several model simulations were run to test the sensitivity of wave response to a reasonable range of values. Although the only explicit output from REF/DIF 1 is wave height, I have defined several additional criteria to determine whether or not the waves have been enhanced. These criteria are maximum height, distance offshore, wave shape, down-line velocity, and length of ride.
- Maximum height is defined as the largest wave height anywhere in the model domain. The distribution of wave heights along the edge of the reef can be further examined through a series of cross-sectional plots [See Figure 3.7].
Figure 3.7: Plot of wave height at successive shoreward steps along the edge of the reef. This view demonstrates the waves response to the reef as the crest progresses down the edge of the reef. Note that wave height increases, this is due to increased shoaling as the water depth decreases. - Distance offshore is determined by the distance of the nose of the reef in the cross-shore direction to the zero contour on the depth grid.
- Wave shape as defined by Galvin ( 1972) is: where Hb is maximum height at breaking, g is the acceleration of gravity, m is the beach slope (reef slope) and T is the wave period. According to Galvin (1972) , a value of K > 0.068 represents a spilling or mushy wave. A value of 0.003 < K < 0.068 represents a plunging or "tubing" wave and a K < 0.003 represents a surging wave [See Figure 3.8].
This parameter was calculated two ways for each model run. One calculation was made using the slope of the shoreface which is 0.03 for all model simulations. Another calculation was made using the toe slope of the reef. These are labeled K1 and K2 in Table 4.
Figure 3.8: Wave types as defined by Galvin (1972). These wave types also correlate with the Iribarren number.
In attempt to further explore predicting wave shape from model results, I also calculated the Iribarren number, or the surf similarity parameters, which is known to describe breaker type (Battjes, 1975). The Iribarren number is calculated as:where m is beach slope, Hb is wave height at breaking, and Lo is the deep water wavelength as calculated by linear wave theory. An Iribarren number > 2.0 predicts a surging wave. An Iribarren number value between 0. 4 and 2.0 predicts a plunging wave and an Iribarren number < 0.4 predicts a spilling wave (Battjes, 1975). Both wave shape parameters are relatively simplistic descriptors which omit many obviously important variables that effect wave shape, probably the most important being wind. I decided wave shape was criterion worth investigation, despite these obvious limitations, because of the importance of wave shape to the quality of surfing waves.
- The down-line velocity describes the speed of the broken part of the wave (the bore) as it progresses along the crest of the wave. By looking at a surface wave plot generated by REF/DIF [see Figure 3.9] I determined that the wave crested remained relatively shore parallel while shoaling and breaking about the reef. This demonstrates that as the wave propagates shoreward and begins to break at the offshore edge of the reef the bore progresses down the crest in opposite directions along the side of the reef [see Figure 3.10], as opposed to breaking along the edges of the reef simultaneously. This characterized the "down-line velocity" (Vdl ) and is calculated as: where wave speed (celerity) in shallow water is described as
and g is the acceleration of gravity, h is water depth, and H is wave height (Denny, 1998). The surfable cross-shore (Xs) and long-shore (Ys ) lengths of the wave can be digitized on the Matlab display of combined wave height and breaker output file plot. The length of the surfable ride is measured as the hypotenuse of the triangle defined by (Xs) and (Ys ). This is the distance from the farther offshore breaking point to the point where the entire wave breaks alongshore (the wave closes out). This distance correlated very closely with the sides of the reef.
Figure 3.9: Surface plot of waves affected by the reef as they progress shoreward. The wave response to the reef is demonstrated by the slight curvature of the wave crests. Note that the crest remain essentially shore parallel through the progression.The reef modeling results are displayed in Tables 1 - 4. The bold reef and REF/DIF parameters identify the parameters that were changed while all others were held constant. The italic wave response data indicate wave responses that I considered interesting, these are discussed more thoroughly below.
Figure 3.10: Illustration of bore progressing left and right along the edges of the reef.
Discussion
As an initial test of the model and to create a control situation, three wave simulations were completed on a planar beach with a slope of 0.03 with the reef absent. Three different wave heights were used in the initial conditions. As expected the waves shoaled as they propagated onshore and broke simultaneously at a constant offshore distance [See figure 3.11]. This confirmed a typical wave response to a shoreface without a reef. It also happens to coincide with the California Coastal Commission's finding that an "oversteepened" beach has resulted "closed out" surf conditions. These waves are characterized by an infinite down-line velocity. Next, a reef was incorporated into the bathymetry and the reef enhanced bathymetries were used for the rest of the model runs.
The incorporation of the reef affected the wave response in some general ways. Assuming that the reef was in water that was shallow enough to initiate breaking, the reef effectively moved the break point offshore and the pattern of breaking was controlled by the reef. This demonstrates the reef-enhanced surfing potential by creating a wave that had a non-infinite down-line velocity. This implies that down-line velocity can be controlled via the nose angle of the reef. In general the reef increased the maximum height at breaking as compared to the planar shore-face wave response. In addition, in no tested cases did the predicted length of the ride significantly exceed the wing of the reef. At the depths tested, the input direction of wave propagation (up to 30° ) had little effect on the wave response to the reef. These general conclusions indicate that with appropriate reef depth and wave height, REF/DIF simulated enhanced surfing conditions with the installation of the reef. Wave response to variations in each reef and model parameter are summarized next.
The first five models runs were designed to investigate wave response to shifting the reef increasingly offshore. The first three models runs pushed the break point of the waves beyond offshore breaking distance of the reefless shoreface. [See figure 3.4]. At 175 meters offshore, the ride length began to decrease because the water depth increased beyond y on the backslope of the reef and the wave stopped breaking. To investigate wave response to larger initial wave at this offshore reef location, I increased the input wave amplitude to 1 meter. This created a longer ride at this distance and also satisfactorily broke waves out to a reef location 200 meters offshore. These simulations clearly demonstrate that the reef effectively extends the breaking point farther offshore to a limit that is dependent on reef height and wave height. It also demonstrates that the line of breaking is controlled by the reef and that the predicted ride length is effected by the depth of reef placement.
Maximum height at breaking was affected most dramatically by offshore reef location, toe angle, wave period, and obviously by increased wave height in the initial conditions. As reef location progressed offshore maximum breaking height increased modestly [See figure 3.12]. Interestingly enough, water depth above the reef seemed to have little effect on maximum wave height up to a threshold depth where breaking shut off. This threshold effect may be result of the critical depth that REF/DIF used to define breaking. Waves larger than 2.3 meters broke beyond the reef at the 175 meter location. The large waves created unsurfable model results based on this offshore location of the reef.
Wave height response to toe angle has some non-intuitive results. Maximum heights were recorded when toe angle measured 65° and 90°. The abrupt reef wall created when toe angle is 90° may explain the increased wave height. However, as the toe angle is gradually reduced the wave height quickly drops off until 65° is reach where wave height increases again. Wave height was not enhanced by a toe angle below 65° [See Figure 3.13]. This may be explained by artifacts created when REF/DIF encountered a abrupt bottom feature such as the reef. These unusual patterns were observed wave height contour maps. There are two possible explanations for this artifact. Wave interference patterns may be produced when REF/DIF propagates a single wave crest over abrupt bathymetry and turns the wave crest into multiple "phase-locked" crests which may interfere with each other. Another possibility is that the unusual pattern is a result of high angle diffraction noise. Because REF/DIF can only propagate waves at ~ 55° to the x-axis, abrupt bathymetry (a reef) can cause REF/DIF to attempt to propagate waves at angle higher than this threshold which may create short waves (patter) which radiate away from the reef (O'Reilly, personal communication). This patter is significantly reduced when the toe angle is reduced below 90°. Perhaps the 65° toe angle represents the position where the interference (pattern) is minimized while the reef effect on wave height is maximized.
The increased wave height response to longer period waves is a predicted result of shoaling. It is know that wave energy flux remains constant as wave propagate and shoal. As celerity decreases and wavelength becomes shorter the height of the wave increases to maintain a constant energy flux. Large period waves also have longer wavelengths and thereby create larger maximum breaking height as the waves crash over the reef.
The two calculated wave shape parameters demonstrate the ineffectiveness wave shape parameters for calculating computer simulated wave response to reef designs used in this study [See Table 4]. The K1 values for the gradually sloping shoreface had values ranging from approximately 0.05 to 0.07. These values bound the critical plunging versus spilling value of 0.068. This suggests that on a planar beach with out a reef smaller waves would plunge while large waves would tend to spill. These results demonstrate that Galvin's (1972) wave shape parameter operates as expected for low angle slopes. The K2 values are all below 0.003 which defines a surging wave in Galvin's (1972) model. Empirical evidence suggests that many of the world's most renown surf breaks (i.e. Pipeline) are formed by a reef with a nearly vertical toe angle. This suggests that although Galvin's (1972) model works for gradually sloping beaches it is ineffective for predicting wave shape on steeply sloped structures. Although the Iribarren number was used effectively to predict wave shape in a CERC study (Smith and Kraus, 1990), the maximum slope tested was 40°. This steep slope created what Smith and Kraus (1990) called a confused wave as a result of strong backflow over the artificial bar. All reefs modeled in this study had a toe angle greater than 40°. Although the Smith and Kraus (1990) study was performed in a wave tank with enclosed sides that may have enhance the backflow problem, this presents a potential concern for the designs modeled by REF/DIF.
The down-line velocity is used as an indicator of how quickly the wave will thrust the surfer forward. There are two distinct wave riding styles that are related to this speed. "Tube-riding" waves are waves with a plunging or "hollow" shape and very rapid down-line velocities. These waves are ridden by surfing into the "pocket", or vortex, under the curl with little or no turning. These waves are ridden straight in an attempt to stay just under the curl without allowing the broken part of the wave overcome the surfer. Waves with a slower down-line velocity allow the surfer to perform more turns or tricks. These waves are known as "workable" waves. The down-line velocity is often dictated by daily conditions, so that one location may provide variable down-line velocities. The model results suggest that down-line velocity is well controlled by nose angle. Down-line velocity was also affected by and extremely shallow toe angle (45°) and larger waves both of which lead to an increased wave speed [See Figure 14]. Several expert surfers who were interviewed suggested down-line velocities ranging from approximately 10 mph to 20 mph.
The length of the ride was maximized when model conditions created a wave that broke along the entire extent of the reef. The ride length never exceeded the length of the wing of the reef. The ride length decreased if the wave conditions resulted in a wave that did not break along the entire wing of the reef. These resulted because the reef was in a water depth such that breaking only occurred along the highest portion of the reef [See Figure 3.15]
Conclusion
The use of REF/DIF 1 to model wave response to reef design and wave climate parameters marks a significant advance over traditional wave ray modeling techniques. Although REF/DIF 1 represents one of the most current monochromatic water waves models to date, one must remember that model predictions are still only qualitative and do not provide direct predictive results. Model shortcomings are of three categories. One group of shortcomings are limitations in the current physical understanding of wave behavior, especially when interacting with a bar or reef and during breaking. The second group of shortcomings are those specific to the limitations of the model, an example is the exclusion of wind on wave behavior. The third category of potential error is the proper application and interpretation of model results. Despite these shortcomings, the modeling of wave response to artificial reef designs has provided some valuable information that may aid in the design and construction of the reef.
The modeling results suggest that the installation of an artificial reef will effectively extend the surf zone offshore and create waves that break with a defined pattern. These factors will enhance the surfing potential in the area. In addition, modeling results suggest that the down-line velocity can be controlled by the nose angle and that a threshold depth exists for breaking to occur. For the conditions simulated this depth threshold is almost equal to the maximum tidal range in the El Segundo area. This suggests that the artificial reef will not create "surfable" waves at all tidal ranges. In order to reduce aerial exposure of the reef (one of the design goals) the reef should be designed to break at lower tides.
Wave shape proved to be a difficult response to predict. The two parameters used to predict wave shape predicted a surging wave for all situations tested. In fact, the parameters measured for this modeling exercise were often outside the given wave shape parameter ranges by more than an order of magnitude. It is difficult to say whether this difference reflects a true potential wave response or suggests that the wave shape models are limited to predicting wave response for low angle structures and natural beaches (where they were developed). It is commonly known that many surfing spots have waves breaking by near vertical reef structures, however it appears no physical model has been developed to predict wave response to such structures.
Despite the shortcomings of wave shape prediction, the REF/DIF 1 model simulation results are in accordance with anticipated physical response to a reef structure. These data suggest that the artificial reef enhance potential surfing conditions by extending the surf zone offshore and producing waves that break in a manner similar to other "surfable" locations. The physical subtleties that determine a quality surfing wave may be lost in the modeling exercise and are potentially beyond the scope of current understanding of wave breaking. Actual wave response will not be understood until the reef is constructed. This will provide an excellent opportunity to investigate the strengths and shortcomings of the above model predictions.