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Draft Journal Paper 6 Feb 02

Wave Transformation Modeling at Cape Fear River Entrance, North Carolina

Edward F. Thompson,M.ASCE and Jane McKee Smith, M.ASCE

ABSTRACT: Wave transformation in the region of Cape Fear, NC, is investigated through the application of the numerical spectral wave model STWAVE. Field measurements of offshore and nearshore directional waves, high-resolution bathymetry, tide, and wind were collected starting in the fall of 2000. Model verification is presented based on two storm events. The root-mean-square error in wave height is approximately 0.2 m and in mean wave direction is approximately 15 deg. The relative importance of the wave model input parameters of bathymetry, tide, wind, and spectral shape (measured versus parameterized) are examined.The related parameters of high-resolution bathymetry and accurate tide elevation are found to be most significant in reducing model error. Use of parametric input spectra gave comparable results to input of measured two-dimensional spectra for the selected storms.

INTRODUCTION

As modeling and field measurement technologies have advanced in recent years, the intricate physical processes typical of exposed ocean coasts have become better understood. Although further advances must be achieved to fully meet the needs of engineers, scientists, and others responsible for coastal applications, the interactions between waves, currents, winds, and shallow bottom can be documented and modeled with increasing confidence.

A large field measurement program underway in the vicinity of the Cape Fear River Entrance, NC, affords an excellent opportunity to evaluate processes around a dynamic entrance and adjacent beaches with a complex exposure to ocean waves. The entrance not only involves strong currents and extensive ebb tide shoals, but also includes major effects due to Frying Pan Shoals, a lengthy feature extending in a southerly direction from Cape Fear and filtering much of the wave energy arriving from the north Atlantic Ocean. The program is funded by the U.S. Army Engineer District, Wilmington, and operated by the U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, Field Research Facility (FRF).

The measurement program was initiated to monitor processes in the area immediately before construction of a new deep-draft entrance channel and for an extended time period after construction. The data also provide much needed in situ documentation of offshore and nearshore processes that has been heretofore unavailable at this site. Previous studies have been forced to rely primarily on offshore hindcasts, which may not fully represent the complex exposures of this area. The hindcasts have been supplemented in some studies by local land-based observations of breaking waves and nondirectional wave data from a National Oceanic and Atmospheric Administration, National Data Buoy Center (NDBC) gauge at Frying Pan Shoals Light with full exposure to the North Atlantic Ocean. Data from the present monitoring program has greatly improved on previously available sources for any applications along the south-facing coast west of Cape Fear.

Taking advantage of the unusually high quality bathymetric data and extensive hydrodynamic data being collected, this paper has two objectives: to advance understanding of local processes, and to evaluate the effectiveness of numerical wave transformation model STWAVE, a standard model used by the U.S. Army Corps of Engineers and others for determining nearshore wave conditions from known offshore conditions. Field measurements are described in the next section, including two storm events selected for detailed study. A brief description of the STWAVE model is given, followed by a detailed explanation of model application to the two selected storms.   The final major section of the paper addresses sensitivity of model results to approximations commonly made in engineering studies due to lack of detailed knowledge at a site or practical limitations of time and study resources.

FIELD MEASUREMENTS

A major field measurement program was initiated in the Fall of 2000 to monitor processes before and after dredging of a reoriented deep-draft entrance channel to Wilmington Harbor, NC. Measurements include detailed surveys of nearshore bathymetry and sustained gauging of waves, water levels, and currents. An outer gauge was positioned to measure wave and water level data seaward of the navigation channel and ebb tide shoals. Multiple nearshore gauges provide data in the vicinity of the navigation channel and along beaches adjacent to the entrance. The field site, measurement program, wave climate, and data from two selected storm events, are described in the following subsections.

Field Site

The Cape Fear River entrance is located along a south-facing segment of the North Carolina coast (Fig. 1). Oak Island lies to the west of the entrance and Bald Head Island to the east. Both islands have active, sandy coastal beaches. Cape Fear is the eastern extremity of Bald Head Island, where the coastline abruptly changes to a north-south orientation. Frying Pan Shoals extends south southeast from the tip of Cape Fear. Frying Pan Shoals are about 25 km long, with minimum water depths of 2 m mllw along most of its length. The tide range is 1.5 m between mhhw and mllw. The entrance to the Cape Fear River is a natural, unstructured inlet with depths in the natural channel enhanced by dredging as needed to maintain a 11.6-m deep-draft navigation channel. The navigation channel extends seaward through large ebb tide shoals. The project to realign and deepen the outer entrance channel to 12.8 m was begun in November 2000. This paper addresses only the original channel configuration, for which detailed, recent surveys are available. This configuration is considered to be sufficiently representative of bathymetry affecting waves during the storm events considered in the paper.

Measurements

Detailed bathymetric data were collected during August and September 2000. Two complementary survey methods were used to get high-resolution coverage of the entire ebb tide shoal and adjacent beach areas. An amphibious LARC equipped and operated by the FRF collected shore-perpendicular beach and nearshore profiles along a 9-km reach of Oak Island and the entire coast of Bald Head Island. Profiles are spaced at intervals of 120-150 m and extend from the beach berm to about 7.6-m water depth. Additional transects provide coverage of shallow parts of the ebb tide shoals. Horizontal control is via a Real-Time Kinematic Global Positioning Satellite (RTK-GPS) survey system. Depth/elevation data are accurate within about 3 cm.

Bathymetriccoverage of the navigation channel and deeper parts of the ebb tide shoals was provided by a LARC-mounted Submetrix Interferometric System, using side-scan sonar to collect depth data with 5-10 cm accuracy. Accurate horizontal control is achieved with RTK-GPS. This system is most effective in water depths of 2-20 m. Hence, it provided good coverage to the seaward extent of the ebb tide shoal complex.

Directional wave, water level, and current data were collected at one offshore location (referred to as the 11-Mile gauge) and two nearshore locations (Oak Island and Bald Head Island), as shown in Figure 1. Water depths are about 13 m at 11-Mile, 6.1 m at Oak Island, and 5.5 m at Bald Head Island gauges. The 11-Mile gauge was placed just south of a proposed dredged material disposal area. All three gauges are Acoustic Doppler Current Profiler (ADCP) instruments accompanied by a pressure transducer. Directional wave spectra are calculated from time series of velocity at various depths obtained by the ADCP. Spectral bin widths are 0.015625 Hz in frequency and 4 deg in direction. Corresponding significant wave height Hm0, peak period Tp, and peak direction Dp parameters are determined from the directional spectrum. Peak frequency represents the highest energy density in the frequency spectrum integrated over all directions. Peak direction is determined as the vector mean at the peak frequency. Water level is determined from the pressure transducer record. Time series of current velocity at the surface, mid-depth, and bottom are also provided from the ADCP gauges. The 11-Mile and Oak Island gauges collect 20-min time series at 3-hr intervals.The Bald Head Island gauge collects 20-min time series at 1-hr intervals.

The 11-Mile gauge operated consistently from initial deployment on 22 Sep 2000 through at least the fourth deployment, ending 12 Jun 2001. The Bald Head Island gauge was operational during the same time period, but experienced occasional data losses for periods of up to several days. The Oak Island gauge was damaged by a trawler on 23 Oct 2000 and not successfully reactivated to date.

An additional ADCP/pressure gauge provides water level and current data at three locations in the Cape Fear River channel.  This single gauge is moved between three deployment sites. As with the other gauges, directional wave spectra and parameters are also provided, though wave energy is low at these protected sites.  The gauge collects 20-min records at 3-hr intervals.

The NDBC wave gauge at Frying Pan Shoals Light is located 45 km southeast of the southeast corner of the STWAVE grid coverage area depicted in Figure 1. It lies on the crest of the extension of Frying Pan Shoals into deeper North Atlantic Ocean waters. Depth at the gauge is 13 m. Depth in surrounding waters, away from the localized shoal, is around 24 m.  NDBC collects hourly significant wave height and period, and wind speed and direction at this site.

Wave Climate

Although the duration of wave gauge operation is limited to date, sufficient data have been collected from the 11-Mile and Bald Head Island gauges to provide insights on wave climate variability and the impact of Frying Pan Shoals.   Wave roses for available data in year 2000 show characteristic differences in wave climate for the two sites (Figure 2).  Dominant wave directions at 11-Mile Gauge are from southeast and south southeast.  At Bald Head Island gauge, dominant directions are shifted to south and south southeast.  These direction shifts between offshore and nearshore locations are consistent with expected effects of wave refraction.

The 11-Mile Gauge wave rose shows a small, but significant component of the wave climate coming from easterly directions.  These waves have passed across Frying Pan Shoals to reach the gauge.  By comparison, a multi-year hindcast wave climate for this area, but seaward of any coastal bathymetry, shows strong wave dominance from east to southeast directions (Thompson, Lin, and Jones 1999).  Frying Pan Shoals filters, but does not eliminate, wave energy reaching the 11-Mile Gauge site from these directions.  Waves from easterly directions are virtually absent at the Bald Head Island gauge. This site is sheltered to the east by the Bald Head Island land mass and to the east southeast by an extremely shallow part of Frying Pan Shoals extending from Cape Fear.

November 2000 Storm

The highest significant wave heights recorded at 11-Mile and Bald Head Island gauges during the first two gauge deployments (22 Sep to 5 Dec 2000) were produced by a storm in late November.  Peak significant heights are 2.48 m and 1.94 m, respectively. A four-day time period encompassing this storm event, 25-28 Nov 2000, was selected for modeling.

Data from 11-Mile and Bald Head Island gauges show the highest wave conditions occurred during about a 12-hr period beginning shortly after noon on 25 Nov (Figure 3). Peak periods during this time period range from 7 sec in the early phase of the storm to 10 sec in the declining phase.  Peak directions at the 11-Mile gauge show wave energy coming from south southeast (150-160 deg) during the initial phase of the storm, shifting to south (175-180 deg) during the declining phase.  Another prominent increase in significant wave height occurs near the end of 27 Nov. Maximum significant heights are around 1.5 m at both gauges, with peak periods of 6 sec and directions from south southwest and southwest.

Significant wave heights at the Bald Head Island gauge equal or slightly exceed those at the offshore gauge for all but the first 1.5 days of the four-day time period. Maximum difference occurs during the storm peak and low tide (0000 EST 26 Nov), when Hm0 is 2.23 m and 1.34 m at 11-Mile and Bald Head Island gauges, respectively.  Peak periods are reasonably comparable at the two gauges. Peak directions at Bald Head Island tend to be confined to a narrower range, about 160-220 deg azimuth, than at the 11-Mile gauge. The collapse of nearshore wave directions into a narrow range centered on the direction perpendicular to local bottom contours is an expected consequence of wave transformation between the two gauge locations.

Frying Pan Shoals severely limits wave energy arriving at the 11-Mile gauge from azimuths of 20-150 deg, so peak wave directions east of south suggest that the 11-Mile gauge is experiencing a diminished remnant of a more energetic wave condition coming from the open ocean east or southeast of the coast. Data from the exposed Frying Pan Shoals gauge show a consistently higher significant wave height than the 11-Mile gauge during the entire 4-day time period (Figure 3). Peak periods are generally comparable except during much of 27 Nov, where a 9-sec wave component impacted the Frying Pan Shoals gauge but not the 11-Mile gauge.

Additionally, Figure 3 includes winds measured at Frying Pan Shoals Light and water depth at the 11-Mile gauge.  Winds are from southeast in the early part of the storm, shifting to from a westerly direction by the beginning of 26 Nov.  Wind speed peaked at 21 m/s at 1500 on 25 Nov and then dropped to less than 15 m/s except for two brief intervals around 0000 27 Nov and 0000 28 Nov.

March 2001 Storm

A major storm impacted the study area in late March 2001. Maximum significant wave heights were 3.2 m and 2.6 m at 11-Mile and Bald Head Island gauges, respectively. Peak period during the most energetic part of the storm was around 11-13 sec.  A four-day time period was selected for modeling of this storm (Fig. 4).

The storm peak occurred at 1800 EST 20 March 2001 at the 11-Mile gauge. The peak appeared at 1944 EST in the hourly Bald Head Island gauge record, indicating that peak conditions occurred in the middle of the 3-hr interval between 11-Mile gauge records. Wave directions at the 11-Mile gauge are from the south southeast to southeast during the storm peak. Starting at 1200 EST 21 March, direction shifts through south to south southwest.  The brief interval of waves coming from the south coincides with a secondary peak in Hm0, reaching 2.2 m at 11-Mile gauge and 1.6 m at Bald Head Island gauge.  Peak periods for this secondary storm event range between about 6 sec and 11 sec, indicating likely contributions from more than one wave system.

Significant wave height at the Bald Head Island gauge is lower than at the 11-Mile gauge for the entire four-day period.  Peak periods are generally comparable between the two gauges. As in the November 2000 storm, peak directions at the Bald Head Island gauge are confined to 160-220 deg, a considerably narrower range than at the 11-Mile gauge.

Wave conditions at Frying Pan Shoals show a similar storm sequence, but maximum Hm0 is over 7 m, more than twice as high as at the 11-Mile gauge. Peak periods during the main storm peak are comparable at all gauges, ranging from 11 sec to 13 sec. The data suggest that peak storm waves are coming from a southeasterly or easterly direction and that they are turned and attenuated by Frying Pan Shoals before arriving at the 11-Mile gauge.  Wind speeds at Frying Pan Shoals rose to a peak of 27 m/s at the storm peak, dropped precipitously by the end of 20 Mar, and then rose to a range of about 10-17 m/s for the next day and a half of the selected interval and dropping under 10 m/s for the final day.  Wind direction was from the east and east southeast during the storm buildup and peak, shifting abruptly to west and west southwest on 21-22 March.  Winds were from the north during the first half of 23 Mar and then from west southwest for the remainder of the day.

WAVE TRANSFORMATION MODEL

The wave model STWAVE has been widely used within the U.S. Army Corps of Engineers and elsewhere for engineering project studies.  STWAVE is an efficient steady-state, finite-difference model designed to simulate the nearshore transformation of a directional spectrum of wave energy.  A typical application is to take known offshore wave conditions, in water depth on the order of 20 m or greater, and transform those incident wave conditions over complex nearshore bathymetry, often to the point of nearshore breaking.  Typical coverage areas are 10-20 km in the offshore direction and 20-40 km along the shore, with grid cell size of 25-100 m. 

STWAVE is described in detail in other publications and only a brief overview is provided in this paper (Smith and Smith 2001; Smith, Sherlock and Resio 2001).  STWAVE is a phase-averaged spectral model based on the conservation of wave action.  Input to the model can include an incident directional spectrum at the seaward boundary (assumed to be uniform along the boundary), local wind speed and direction (assumed to be uniform over the model domain), and a current field over the model domain (assumed to be uniform with depth).  Wave breaking due to wave steepness and/or shallow depth is included in the model.  Nonlinear wave-wave interactions, though often small on the scale of STWAVE domains, can be optionally invoked.  Other assumptions and limitations in the model include:  only landward-moving wave energy, negligible wave reflections, mild bottom slope, linear refraction and shoaling, and negligible bottom friction.

Output from STWAVE includes wave parameters Hm0, Tp, and Dp over the entire model domain and directional spectra from selected points.  Peak wave period Tp is the reciprocal of peak frequency fp, which is the frequency at which the highest energy density occurs in the frequency spectrum integrated over all directions.  The wave direction Dp as defined in STWAVE is the vector mean from the integrated spectrum.

MODEL APPLICATION TO SELECTED STORMS

The two storms selected for modeling provide a variety of wave and wind conditions, which form a good basis for evaluating STWAVE.  Procedures used to set up STWAVE for the Cape Fear River Entrance region and to simulate the selected storms are described in the following subsections.  Model results for the two storms are also discussed.

Wave Model Coverage Area and Bathymetry

Coverage area for the STWAVE model grid is usually determined by balancing several considerations.  Coverage is a rectangular box subdivided into uniform size, square grid cells.  Grid cells must be small enough to adequately resolve all bottom features important for wave transformation.  Similarly, coverage area must extend offshore and alongshore far enough to encompass all bottom features important for wave transformation to the study area.  Also, the seaward grid boundary must be in deep enough and smooth enough bathymetry that the assumption of a uniform incident wave condition along the boundary is reasonable.  These physical concerns must often be balanced against STWAVE computational demands, which are directly related to the total number of grid cells.  For this study, the STWAVE grid coverage area was 21.4 km in the offshore direction by 40.0 km in the alongshore direction, with a resolution of 50 m (Fig. 1). The offshore boundary has an east-west orientation and passes through the 11-Mile gauge location.  The east boundary was placed just east of Frying Pan Shoals.  In terms of the number of cells, the grid is 429 by 800, for a total of 343,200 cells.  This relatively large grid was impractical for running on a PC platform, so all simulations for this study were done with a parallelized version of STWAVE at the US Army High Performance Computing Center.

Bathymetry data were obtained from National Ocean Survey (NOS) nautical chart sources, as used in a previous study (Thompson, Lin and Jones 1999).  In areas covered by field surveys discussed earlier, NOS data were replaced with survey data. These data were then interpolated to the STWAVE grid.

Incident Wave Spectra

Directional wave spectra from the 11-Mile gauge provided incident spectra at the offshore boundary of the STWAVE grid.  Water depth along this relatively long boundary is reasonably constant (with the exception of Frying Pan Shoals), ranging from 13 m at the 11-Mile gauge to 16 m at the western edge of the boundary.  In this application, 21 spectral frequencies were used ranging from 0.015625 Hz to 0.328125 Hz, in increments of 0.015625 Hz. These frequency bands match those of the 11-Mile gauge.  STWAVE directions range from 95 deg azimuth to 265 deg azimuth in 5-deg bands.  Since the 11-Mile gauge spectra cover a full 360 deg range in 4-deg bands, gauge directional energy was truncated to fit STWAVE direction constraints and interpolated to fit the 5-deg STWAVE bands.

Water Levels

Bathymetry in the STWAVE grid was referenced to mllw.  An adjustment from this water level was determined at each simulation time based on the difference between water level measured at the 11-Mile gauge and mllw.  The adjustment was applied uniformly over the entire STWAVE grid.

November 2000 Storm

STWAVE model results from grid points at the 11-Mile and Bald Head Island gauge locations during the November 2000 storm are shown along with gauge parameters in Figure 3.  At the 11-Mile location, STWAVE and gauge Hm0 are nearly identical, except for the first three simulation times, indicating that all appreciable wave energy measured at the gauge was traveling toward shore and was included in the direction range accommodated by STWAVE.  Peak periods and directions at the 11-Mile location are reasonably comparable, but differences in the spectra and parameter definitions give rise to some differences during the 4-day simulation period. 

 Bald Head Island STWAVE Hm0 results are reasonably close to gauge data.  However, STWAVE results are more controlled by incident wave parameters and do not capture some details of gauge results.  For example, the STWAVE Hm0 around the storm peak shows a double peak, reflecting the pattern of incident waves, while the Bald Head Island gauge shows only one peak.  Two lower peaks occurring later in the simulation time period (at the beginning and end of 27 Nov) show Hm0 higher at the Bald Head Island gauge than at the 11-Mile gauge.  STWAVE does not capture this behavior.  Peak wave periods at Bald Head Island STWAVE, 11-Mile STWAVE, and Bald Head Island gauge are generally similar, indicating that the same wave system is dominating both the offshore and nearshore locations.  Peak wave directions at the Bald Head Island location from STWAVE match the gauge quite well, falling within the band of erratic variation in the gauge data.  STWAVE was very effective in modeling wave direction changes between incident waves and this nearshore location.

Differences between time-paired wave parameters over the 4-day period for STWAVE simulation versus Bald Head Island gauge are quantified in Table 1. Mean Hm0 in the simulations is 0.12 m lower than in gauge data.  Mean STWAVE Tp is 0.3 sec greater than in gauge data.  Mean STWAVE Dp is 191.3 deg azimuth versus 193.3 deg azimuth at the gauge, giving a difference of –2.0 deg.  Thus, simulated waves at the Bald Head Island location tend to come from slightly more southerly directions, as compared to the gauge.  Root-mean-square (rms) errors of model versus gauge are also given in the table.

Though the parameter differences are small, they can have amplified implications for longshore transport Q calculations.  To give insight on the impact of model versus gauge differences on potential longshore transport, Q was calculated from model and gauge parameters with the standard CERC formula (e.g. Shore Protection Manual 1984).  Mean difference is 274 m3/day, but rms error is 2782 m3/day, a relatively large value considering that mean Q is around 2000 m3/day (Table 1). The time history of Q during the storm event is shown later in the paper.

March 2001 Storm

STWAVE model results during the March 2001 storm are included in Figure 4. As with the earlier storm, Hm0 values are nearly identical for model and gauge at the 11-Mile location, indicating that the STWAVE incident spectrum encompassed all significant energy except for the first few cases at the beginning of the first day.  As before, differences in model and gauge spectra and parameter definitions give rise to some differences in Tp and Dp over the four days. 

Model and gauge Hm0 mean difference during this event is only 0.05 m, with rms error of 0.22 m (Table 2). Model time history of Hm0 follows the gauge time history quite well for this event.  Since STWAVE Tp at Bald Head Island match that at the 11-Mile location, differences in STWAVE versus gauge Tp at Bald Head Island are reflective of incident spectrum and parameter definition differences more than any model-induced changes during transformation.  Several interesting cases on 23 March, when 11-Mile and Bald Head Island gauges reported very different values of Tp , are successfully captured by STWAVE.  Mean and rms errors in Tp are 0.3 sec and 1.6 sec, respectively.  Mean Dp is 194.6 deg for STWAVE versus 185.7 deg for the gauge at Bald Head Island.  This difference is considerably larger than for the November 2000 storm and of opposite sign.  The rms error is 15.1 deg.  The effect of parameter differences on Q is a mean error of  ‑595 m3/day and rms error of 4897 m3/day.

Directional spectra are available from STWAVE and the gauges.  Many of these spectra were plotted to gain further understanding of both the November 2000 and March 2001 storm events.  Spectra from two times during the March 2001 storm illustrate the comparisons.  Spectra from 1800 20 Mar correspond to a time of peak Hm0 and strong winds from the east, as recorded at Frying Pan Light (Figure 5). In the plots, frequency increases from 0.015625 Hz at the innermost arc to 0.328125 Hz at the outermost arc.  Most energy at the 11-Mile gauge is at relatively low frequency coming from southeast.  However, high-frequency energy from easterly directions is also clearly included.  At the Bald Head Island gauge, a small remnant of high frequency energy from the east southeast is visible, but most energy is coming from southerly directions.  The main energy concentration has split into two directional concentrations, coming from around 15 deg east and west of south. 

Since strong local winds are included in the gauge spectra shown, STWAVE spectra for comparison were generated in model runs that included local wind input and activated source terms.  The STWAVE spectrum at Bald Head Island shows the model captures the main rotation of incident direction from southeast to south.  The model did not capture bifurcation of energy into two directional groupings.  This split and some other details of the gauge spectra may not be statistically significant and stable, since they are not consistently shown in successive hourly gauge spectra.  The STWAVE spectrum at the location of the now inoperative Oak Island gauge is also shown.  It is very similar to the model spectrum at Bald Head Island.

Another directional spectrum comparison is for 1800 21 Mar (Figure 6). This time is around the second peak of Hm0 during the four-day simulation.  It is also a time of strong local winds from westerly directions.  The 11-Mile gauge spectrum shows the main energy concentration coming from 200-210 deg and high frequency energy from westerly directions.  As with the Bald Head Island gauge, model spectra at both Bald Head Island and Oak Island show little change in the primary incident direction during nearshore transformation.  STWAVE spectra also show evidence of high frequency energy from southwesterly directions.

SENSITIVITY TO WAVE MODELING CHOICES

Overall, model simulations of the two storm events are reasonably good.  However, it is worthwhile to examine some aspects of the model application which could have been done differently.  For example, STWAVE source terms were not invoked in the previous comparisons (with the exception of directional spectral plots presented).  Source terms lead to more complicated model inputs and slower run times but may improve model results.  Also, some aspects of the STWAVE base application include more accurate inputs than would normally be available in routine studies.  The impact of these more accurate inputs on model results is of interest for future studies.  Model sensitivity to application choices and procedures was evaluated with additional STWAVE simulations of the two storms.  Simulations presented in the previous section are considered the base case.  The sensitivity simulations and results are discussed in this section.

Bathymetry

The base simulation took advantage of detailed bathymetric surveys of the ebb tide shoals and adjacent beaches.  Normally, such detailed, recent, high-quality data would not be available for a study area.  For example, in a recent past study of this area, only the standard NOS databases for STWAVE grid bathymetry were available (Thompson, Lin and Jones 1999). 

 An STWAVE grid identical to that in the base simulation but with depths taken only from the NOS database was constructed.  Simulations for both storm events were repeated with no other changes.  Difference statistics are given in Tables 1 and 2.  Parameters during the larger storm event, March 2001, are plotted along with the base case in Figure 7.  The change in bathymetry clearly impact Hm0 , Tp , Dp , and Q during parts of the event.  As previously, Q results shown for the Bald Head Island gauge were calculated from wave measurements, not measured directly.

Incident Wave Spectra

Typically, STWAVE incident waves are obtained by reconstructing a directional spectrum to fit known Hm0 , Tp , and Dp parameters.  The TMA frequency spectrum and cosine to the n’th power form of directional spreading are used (e.g. Smith and Smith 2001).  Using this technique, incident wave conditions for both events were reconstructed from parameters at the 11-Mile gauge.  Making only this change to the base case, the two events were rerun. Difference statistics are given in Tables 1 and 2 and the time history for the March 2001 storm is included in Figure 7.  The error statistics show relatively little difference between using parameteric spectra and measured two-dimensional spectra, although directional error increases with use of parametric spectra.  Differences are expected to be greater at times when multiple wave trains are present and a single parametric height, period, and direction may not be representative of the incident waves.

Water Level

Water level in STWAVE simulations is typically chosen as a constant value.  In the base case of this study, measured water levels based on data from the 11-Mile gauge were used.  To assess the impact of using a constant water level, the STWAVE runs were repeated three times with water level fixed at mllw, msl, and mhhw.  All other conditions matched the base case.  Difference statistics are given in Tables 1 and 2 and the time histories for the March 2001 storm is given in Figure 8.  Water level systematically impacted results, especially during the higher energy part of the 4-day simulation.  The figure illustrates the range of scatter, which is especially large for Q.

Model Source Terms

The STWAVE model is typically used to transform waves over a relatively short distance from open ocean to a coast.  Model source terms are bypassed and only propagation terms are included.  For two reasons, source terms are potentially more important in this study.  First, the grid domain in this study is larger than usual, so wave-wave interactions during propagation may have more impact. Second, parts of the nearshore waters around Cape Fear River Entrance are unusually well-protected from ocean waves and local wave generation may be more significant to the wave climate than at most other ocean sites. 

The impact of source terms was evaluated by rerunning the two storm events twice.  In one set of simulations, source terms were activated but no local wind was included.  In the other set, source terms were activated and local wind, as measured at Frying Pan Shoals Light, was included.  All other aspects of the runs matched the base case.  Difference statistics are given in Tables 1 and 2.  Time history comparisons are shown for the November 2000 storm, since onshore local winds were more prevalent in that storm than in the March 2001 storm (Figure 9).

SUMMARY AND CONCLUSIONS

The two objectives of this study were to gain insights into local hydrodynamic processes and to evaluate numerical wave model performance for the complex area around Cape Fear River entrance.  Wave gauge data are summarized over a two and one-half month time period and examined in detail during two 4-day storm events.  Factors clearly affecting local waves include transformation over ebb tide shoals and other shallow bottom areas, filtering and/or blocking of wave energy by Frying Pan Shoals, and wave generation by local winds.

The numerical wave model STWAVE was used to simulate wave conditions and compare results at a 5.5-m deep location near Bald Head Island based on known directional wave spectra in 13-m depth offshore and local winds measured at Frying Pan Shoals Light.  Two 4-day storm events were simulated.  Sensitivity to wave modeling choices was examined by modeling the storms eight times, with variations in model input each time.  All of the variations produced reasonable results in comparison to the Bald Head Island gauge.  However, differences were large enough to confirm that modeling should be performed with as much care and accuracy of inputs as is reasonably possible in studies.  Differences in potential longshore transport rate were especially large among the model scenarios considered.  Accurate bathymetry had the most significant impact in reducing the rms error between model results and measurements (20 percent reduction in rms error).  Differences presented in this paper are highly dependent on the particular events considered, the local site, and the particular nearshore gauge location where model versus gauge comparisons could be made.  However, these results do give important insights on the range of variations that may be introduced by choices made in preparing model inputs.

ACKNOWLEDGEMENTS

The tests described and the resulting data presented herein, unless otherwise noted, were obtained from research conducted under the Transformation-Scale Waves Work Unit, Coastal Navigation Hydrodynamics Program, of the United States Army Corps of Engineers by the Engineer Research and Development Center, Coastal and Hydraulics Laboratory (CHL). Ms. Ann Sherlock, CHL, assisted with adaptation of the parallelized version of STWAVE to this project.  Mr. H. Carl Miller, CHL, is the Coastal Monitoring Program Manager for the Wilmington Harbor Navigation Project.  Dr. Robert E. Jensen and Ms. Mary A. Cialone, both of CHL, provided helpful review comments. Permission was granted by the Chief of Engineers to publish this information.

REFERENCES

Smith, J.M., Sherlock, A.R., and Resio, D.T.  (2001).  “STWAVE:  Steady-state spectral wave model user’s manual for STWAVE, Version 3.0.” Special Rep. ERDC/CHL SR-01-1, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss.

Smith, S.J., and Smith, J.M.  (2001).  “Numerical modeling of waves at Ponce de Leon Inlet, Florida.” J. Wtrwy. Port, Coast., and Oc. Engrg., ASCE, 127(3), 176-184.

Shore Protection Manual.  (1984).  4th ed., 2 vols, US Army Engineer Waterways Experiment Station, Coastal Engineering Research Center, US Government Printing Office, Washington, DC.

Thompson, E.F., Lin, L., and Jones, D.L.  (1999).  “Wave climate and littoral sediment transport potential, Cape Fear River Entrance and Smith Island to Ocean Isle Beach, North Carolina.” Tech. Rep. CHL-99-18, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss.