Estimating Overtopping Impacts in Los Angeles/Long Beach Harbors with a Distorted-Scale Physical Model


David D. McGehee, P.E., M.ASCE,[1] Chuck Mesa, P.E.[2],

and Robert D. Carver, M.ASCE[3]


ABSTRACT:   Recent topographic surveys of the breakwaters for Los Angeles/Long Beach Harbors revealed an average crest elevation of the San Pedro Breakwater of approximately 1.5 ft below the design crest of + 14 ft MLLW. A physical model study was conducted to estimate future impacts on harbor operations if crest loss continues or if the crest is restored to the design elevation. A 3‑dimensional distorted-scale physical model (1:100 vertical, 1:400 horizontal) was used to investigate the change in total energy and low frequency wave energy (periods > ~85 sec) at numerous locations within the harbor as a function of the breakwater crest elevation. Constraints of the distorted scale model were overcome to generate incident overtopping waves that induced low frequency oscillations in the harbor. Sensitivity of these oscillations to crest elevation is presented.



The San Pedro breakwater is the westernmost component of the three breakwaters that protect the Los Angeles/Long Beach Harbor (LA/LB) complex. A survey of the entire three-breakwater system was recently performed (USACE 1996) that revealed the San Pedro Breakwater is between 1 to 3.5 ft below the + 14 ft MLLW design elevation. The causes are not known at this time, nor is it known whether settlement will be progressive. However, the protection level afforded to the harbor is reduced, relative to the design elevation. Of particular concern is the potential for impacts on Port operations from increased long wave energy levels at various terminals inside the harbor. The present study was designed to address two questions:


1. Does the present condition of the breakwater result in significantly more low frequency energy in the harbor, relative to a structure at the design crest elevation?

2. What are potential future impacts on low frequency energy in the harbor if crest elevation loss continues?


The amplitude of incident long waves at the prototype scale is negligible relative to the breakwater dimensions, so it is expected that the crest elevation will have little or no effect on direct transmission of low frequency wave energy until the crest approaches the still water level.  Overtopping of the breakwater by wind waves is common during high energy sea states, and the amount of wave energy transmitted into the harbor by overtopping is a function of crest elevation.  Low frequency wave energy in the harbor has been strongly correlated with wind wave energy offshore (Seabergh, 1999), so it is reasonable to question if increased overtopping wind waves will affect low frequency wave energy in the harbor.


A 3-d physical model of the LA/LB has been in use at the US Army Engineer Research and Development Center (ERDC) since 1973 to investigate many effects of harbor modifications on tidal circulation and harbor resonance (Seabergh, 1993). Previous harbor resonance studies utilizing this model produced low-amplitude long waves with the wave generator that propagated throughout the harbor.  In the present study it was desired to generate energetic wind wave spectra capable of overtopping the breakwater, and measure the resulting low frequency wave energy in the harbor as a function of various crest elevations. Due to model scale and wave generator limitations, this study required developing a testing program that could adapt the model to a purpose not intended in its original design.



Model Description      

The Los Angeles and Long Beach Harbors model is molded in concrete grout at a vertical scale of 1:100 and a horizontal scale of 1:400 and reproduces San Pedro Bay and the Pacific Ocean seaward of the harbor out to the -91.5-m (-300-ft) MLLW contour. Model wave data were collected at two sites between the wave paddle (Gages 21 and 24) and the harbor, and at 28 locations throughout the harbor (Figure 1). 


            The LA/LB model breakwater was originally constructed with an impermeable crest at an elevation of +14 ft MLLW (prototype), made from concrete cap segments, placed on top of a permeable rubble base. A survey conducted at the beginning of the study showed the model crest elevation ranged between +13 to +14 ft MLLW, indicating some settlement had occurred over the years. The first two test series were run using this construction method. To test a wide range of crest elevations more efficiently, the concrete segments were removed and replaced with segments made from high-density, water resistant clay. The clay crest segments were easy to shape for any desired crest elevation and could be placed rapidly by hand.




Figure 1.  Model layout with wave gage locations



            In all previous studies of harbor resonance in the LA/LB model, non-overtopping long waves were generated by the wave generator. The ideal plan would generate scaled wind waves energetic enough to overtop the breakwater, and measure the resulting long wave energy in the harbor for various crest elevations.


Seabergh (1993) describes how similitude is obtained in a distorted model by assuming the shallow water approximation for celerity. Using this assumption the effects of the distortion on refraction for waves with periods over 85 sec (prototype) can be neglected, and the time scale can be shown to be 1:40 for long waves, with an error of under 1 per cent. The error in this assumption increases with increasing depth or decreasing wavelength, and would be quite large for the wind wave portion of the spectrum. Physical limitations of the wave generator rendered this potential distortion error moot. Stroke and command signal limitations made the generator incapable of generating high frequency waves with sufficient height to overtop the structure. Preliminary tests determined that the lower limit of wave periods for waves high enough to overtop (O 10 ft prototype scale wave height) was 62.8 sec at prototype scale. Such high energy-long period overtopping waves are extremely unlikely to occur naturally. The decision to proceed with the tests within these constraints was based on the following considerations and assumptions:

1.   The incident waves will introduce wave energy into the harbor that varies with breakwater crest elevation.

2.   Initial tests confirmed that these incident waves, just as wind waves in the prototype, produced oscillations in harbor basins at resonant frequencies well below the incident wave frequencies -  frequencies consistent with those measured in previous model studies

3.   Measured harbor energy will be normalized by incident energy. Trends in amplification of incident energy with crest elevation and incident wave energy at each site will be similar as for wind waves. By normalizing the amplifications again by the amplification at the existing crest elevation, the relative sensitivity of the amplification at any site to future changes in crest elevation can be obtained. Conversion of incident or harbor energy to prototype scale is neither valid nor required.

4.   Overtopping low frequency waves in the model transmit much more energy than overtopping wind waves of the same height, so they provide an upper limit for the prototype situation. If the effect of crest elevation is relatively small at a site for this study, then it will not likely be significant for wind waves in the prototype.



Testing Protocol

Incident Waves    Incident waves were generated with a JONSWAP spectrum having a peak model period of 1.57 sec and a gamma of 3.3. Five intensities of the spectra, corresponded to electronic gains of 10, 20, 30, 40, and 50 percent of full gain, were used which produced wave heights at Gage 21, in 2 ft of water directly in front of the generator, of 0.02, 0.04, 0.06, 0.08,  and 0.10 ft. This produced conditions which range from relatively calm to major overtopping. Two repeat tests were conducted for each combination of crest elevation and gain level.


Breakwater Plans     A total of 9 plans were tested, Table 1. Plan 0 was the existing condition of the model. In Plan 1the model crest was manually corrected to an average elevation +12.5 ft.

Plans 2-7 were conducted with the clay crest set from 0 ft MLLW (overtopping occurs for all gain levels) to + 24 ft MLLW (no overtopping for any gain level). Plan 8 used the same crest elevation as Plan 7, but also eliminated wave transmission through the entrance channel by blocking the opening to Angel’s Gate and the passage between the Middle Breakwater and Pier 400 (see Figure 1), so the only energy entering the harbor came through the porous breakwater.


Table 1.  Summary of Breakwater Plans











Crest (ft) MLLW

+ 13.5*









Crest Material










*   Original construction   ** Entrances blocked



Uncertainty      The two major sources of uncertainty in the results are random errors in the generating/measurement system and model distortion effects in the scaling relationships. Generally, wave height measurements repeat within + 5 percent and the wave generator reproduces the desired command signal within + 3 percent. Since measured wave height at each gage linearly related to the command signal (see Figure 2, below) the maximum uncertainty in wave height measurements can be calculated to be about 3 per cent. Seabergh, 1993, estimated the distortion error in the calculated time scale based upon the shallow water approximation for wave celerity. The time scale ratio of 1:40 obtained from the approximation overpredicts the prototype period by 0.5 % for a 2.125-sec (85-sec prototype) waves in 1 m of water, compared to the exact, intermediate water wave solution. By the same criterion, the maximum error for a 62.8-sec wave is 1.2 per cent.



Total Energy   The total energy measured at a site is characterized by the Hm0. Figure 2 (l) is an example plot of model Hm0 as a function of gain at Gage 5 for all repeat tests of Plan 0. Most of the repeat tests at each gain are within the 3 percent error bars of each other. Generally, all of the gages and all of the plans show a similar clustering of repeat test data and the linear model response as the incident wave heights are increased. For visual clarity, the remaining analysis will plot just one test for each crest/gain combination, and will focus on Plans 2-8 only.


            Gages located behind the breakwater in the outer harbor away from basins – Gages 1, 2, 18 and 20 – best demonstrate the expected trend with crest elevation and gain. Gage number 20, (Figure 2r) is typical of this group: energy decreases with increasing crest height and decreasing wave height, and cessation of major overtopping is evidenced by the flattening of the slope.


*   Existing elevation of prototype structure    

 ** Blocked entrances

Figure 2 - (l) Hm0 vs. gain, Plan 0, Gage 5; (r) Hm0 vs. crest elevation, all plans, Gage 20



            Hm0 amplification (Hamp) is the ratio of Hm0 at each gage to the measured incident Hm0 at Gage 21 for that run. It allows non-dimensional comparison of total energy between sites. To compare the sensitivity of the energy level at a site to changes in crest elevation, amplification was normalized (Hnrml) by dividing by the amplification for the existing condition (Plan 5) for that run. A value of Hnrml less (greater) than 1 means the total energy at that site is decreased (increased) relative to the existing conditions. Figure 3 (l) plots Hamp and Figure 3(r) plots Hnrml for Gage 20. The trend is identical to Figure 2, but the relative order of the gain curves is reversed because of increasing losses associated with breaking and friction at higher gains. There is significant energy reduction as the crest elevation increases from 0 to + 7.5 ft, moderate improvement as the crest increases to the existing elevation of +12.5 ft, little additional benefit in increasing the crest beyond this elevation except for at the highest gain level, and only slightly more benefit in closing off the entrances altogether (Elev. 24B). This is because a significant amount of energy is transmitted through the porous structure.


Figure 3 - (l) Gage 20 Hm0 amplification; (r) normalized amplification


            Note that Hamp > 1 for three cases, but transmitted energy does not actually exceed incident energy at these sites. Though the formula for Hamp looks similar to that for the transmission coefficient, Kt, they are not identical because Hm0 at gages near harbor structures includes a significant amount of reflected, in addition to the transmitted, energy.


            Almost all gages show the same general trends seen in Figures 2 and 3: Hm0, Hamp and Hnrml curves are nearly parallel for the five gain levels. This allows use of the site-averaged Hamp and Hnrml to succinctly characterize the harbor’s overall sensitivity to changes in the crest elevation. Figure 4 is the average Hamp and Hnrml for all interior harbor gages (3-17, 25-28 and 30). Interior harbor gages exhibit the trends seen above, but with one interesting difference: all show an increase in relative energy at the higher crest elevations, and some even continue to increase when the entrances are blocked. While the observation of this “harbor paradox” is not without precedent (Miles and Munk, 1961), it is curious is that the breakwater appears to have “settled” into a low energy state that is only slightly more energetic than an enclosed harbor.



Figure 4 - (l) Average interior harbor Hm0 amplification; (r) normalized amplification


Low Frequency Energy    The spectrum at any gage in the harbor is dominated by the energy at the peak frequency of the incident waves – 0.64 Hz – but includes energy above and below the peak. The main objective of the study is to examine the response of the harbor basins at frequencies below the (unrealistically) high-energy peak. The low frequency portion of the energy spectrum is defined as all energy at or below 0.47 Hz (lower than 85-sec period, prototype). For most of the gages, the sum of the low frequency energy follows the same general trends seen in Figures 2. Low frequency amplification (Lamp) is the square root of the ratio of measured low frequency energy at a site to the measured low frequency energy at Gage 21, and Lnrml is Lamp normalized by Plan 5 Lamp. Plots of Lamp and Lnrml at each gage are not always as well behaved as Gage 20 (Figures 3), but the general trend is preserved. Figure 5 shows the average Lamp for all gains and the average Lnrml for Plans 3 – 7 for the interior harbor gages. (Plans 2 and 8 are omitted for simplicity, as they are unlikely to ever occur in nature). 


Figure 5 – (l) Average low frequency amplification; (r) average normalized low frequency amplification for interior harbor gages


            Sites 5, 7, 11, 13, 16, 25 and 30 are particularly responsive compared to other sites, while Sites 3, 4, 14, 17, and 28 exhibits relatively low excitation. The normalized amplification highlights the sensitivity of the site to changes in the crest elevation. Sites 17 and 28 would react strongly to additional crest loss; Sites 11 and 13 react to a much less degree. Most of the sites are relatively insensitive to positive or negative changes on the order of a few ft.


            Figure 6 plots the Lamp for Plan5, the existing condition, together with the normalized amplification for Plans 3, 4, 6, and 7. (Lnrml for Plan 5 is 1.0, by definition, so it is omitted for clarity). The gages are reordered by decreasing Plan 5 amplification. This allows identification of the few sites that showed changes of a significant magnitude with changes in crest height.


            Sites 5 and 30, while energetic, would experience changes no more than 10 percent. Sites 11 and 13 are only moderately energetic, but loss of crest elevation increases their response by 30 to 50 percent. Site 30 and, particularly, Site 17, are very sensitive to crest elevation. Loss of an additional 2 ½ ft of crest would make Sites 30 and 17 about as energetic as Site 13 and 11, respectively, are now with the existing crest elevation. Note the increase in energy at the two higher crest elevations by some gages, especially at Gage 28.  


            Only Sites 16 and 11 show a significant reduction in energy when the crest is raised to its design elevation, +14 ft MLLW. The rest show reduction, no change, or even a slight increase.


Figure 6.  Lamp (Plan 5) and Lnrml (Plans 3, 4, 6, and 7)




1. The LA/LB model is able to generate low frequency waves that overtop the San Pedro Breakwater at its current crest elevation.


2. The overtopping waves produce low frequency oscillations in the various harbor basins. The energy in the basins increases linearly with incident energy and is sensitive to crest elevation.


3. The average total energy inside the harbor decreases as crest elevation is raised, reaches a minimum near a crest elevation of +12.5 ft MLLW, and then increases for higher elevations. Average measured energy inside the harbor for the existing crest elevation is no more than 10 per cent higher than the configuration with no overtopping allowed and the harbor entrances blocked.


4. Sites with the highest low frequency amplification are relatively less sensitive to crest elevation. Sites with the most sensitivity have relatively less low frequency amplification.


5. Sites 11, 13, 28 and 17 would experience significant increase in low frequency energy if the crest loss continued to an elevation of +10 ft MLLW.


6. Sites 5 and 11 would experience modest reductions in low frequency energy if the crest elevation was raised to +14 ft MLLW.    





            Funds for this study were provided by the San Pedro Breakwater Operations and Maintenance Study of the US Army Engineer District, Los Angeles. Messrs. John Heggins, Tony Brogdon and Tim Nicely of ERDC operated the LA/LB model and collected and reduced model data. Assistance with report preparation was provided by Ms. Allison Dunford of Alatar Enterprises.




Conversion Factors, non-SI to SI Units of Measurement



To Obtain







degrees (angular)





McGehee, D.D., 2001, “3-Dimensional Hydraulic Physical Model Evaluation for the Los Angeles/Long Beach Harbor Operation and Maintenance Study,” Final Technical Report, Emerald Ocean Engineering, Pensacola, FL. 26 p, plus Appendices.


Miles, J.W. and Munk, Walter, 1961, “Harbor Paradox,” Journal, Waterways and Harbors Division, Proc. ASCE, Vol. 87, pp 111-130.


Seabergh, William C. and Thomas, Leonete J., 1999, Los Angeles and Long Beach Harbors Model Enhancement Program: Long Waves and Harbor Resonance Analysis, Technical Report CERC-99-20, US Army Engineer Waterways Experiment Station, Vicksburg, MS. 56 p.


Seabergh, William C. and Thomas, Leonetee J., 1993 Los Angeles and Long Beach Harbors Model Enhancement Program, Improved Physical Model Harbor Resonance Methodology, Technical Report CERC-93-17, US Army Engineer Waterways Experiment Station, Vicksburg, MS. 32 p., plus Appendices.


U.S. Army Corps of Engineers, Los Angeles District, 1996, Comprehensive Condition Survey, San Pedro Breakwater, Los Angeles Harbor, Los Angeles County, CA.



Estimating Overtopping Impacts in Los Angeles/Long Beach Harbors with a Distorted-Scale Physical Mode


Key Words




crest loss

low frequency waves

physical model

harbor oscillations

Los Angeles Harbor

San Pedro Breakwater


[1] Principal, Emerald Ocean Engineering, 107 Ariola Drive, Pensacola Beach, Fl 32561,


[2] Coastal Engineer, US Army Engineer District, Los Angeles, 911 Wilshire Blvd, Los Angeles, CA 90017‑3401 Attn: CESPL‑ED‑D 


[3] Research Hydraulic Engineer, US Army Engineer Research and Development Center, 3909 Halls Ferry Rd., Vicksburg, MS 39180,


[4] Complete study results, including plots of all measurements, can be found in the McGhee, 2001