The Effects of Surface Gravity Waves on High-Frequency Acoustic Propagation in Shallow Water

Transcription

1 IEEE JOURNAL OF OCEANIC ENGINEERING 1 The Effects of Surface Gravity Waves on High-Frequency Acoustic Propagation in Shallow Water Entin A. Karjadi, Mohsen Badiey, Member, IEEE, James T. Kirby, and Cihan Bayındır, Student Member, IEEE Abstract A realistic 2-D time-evolving ocean surface model has been combined with an existing acoustic ray-based model to simulate the effects of sea surface roughness on acoustic wave propagation in coastal regions. Rough sea surface realizations are generated and used as sea surface boundaries in the acoustic model. An approach to achieve high resolution and accurate results while maintaining computational efficiency of a ray-based model is applied. The results are then compared against a unique set of experimental data collected in 15-m water depth in Delaware Bay. These data include simultaneous environment and acoustic propagation (1 18 khz) measurements. Modeled arrival time-angle fluctuations compare well with data and suggest that there are physical processes which need to be included to improve the model, such as bubbles and turbulence as well as 3-D scattering effects. Index Terms Acoustic propagation, acoustic scattering, sea surface waves, shallow water. I. INTRODUCTION T HERE are several environmental parameters that can influence acoustic wave propagation in the ocean, such as water temperature, salinity, as well as sea bottom and surface conditions. Understanding the impact of each individual parameter on the acoustic wave propagation is a necessary step in both determining performance level of underwater acoustic communications and developing techniques for using acoustic signals to predict physical parameters in the ocean. Surface waves are among several environmental parameters that can have apparent influence on underwater acoustic propagation. When an acoustic wave interacts with rough sea surface, acoustic wave scattering will occur. This scattered sound field consists of coherent and incoherent components. In acoustic wave scattering theory, the scale of ocean surface roughness is Manuscript received August 03, 2010; revised June 20, 2011; accepted September 09, This work was supported by the U.S. Office of Naval Research (ONR) under Grant N and in part by the University of Delaware Sea Grant. Associate Editor: J. F. Lynch. E. A. Karjadi and M. Badiey are with the College of Earth, Ocean, and Environment, University of Delaware, Newark, DE USA ( karjadi@udel.edu; badiey@udel.edu). J. T. Kirby is with the Center for Applied Coastal Research, University of Delaware, Newark, DE USA ( kirby@udel.edu). C. Bayındır is with the Department of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA USA ( cihanbayindir@gmail.com). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JOE usually specified by the surface roughness (Rayleigh) parameter which is defined by [1], where is the acoustic wave number, is the root-mean-square displacement of ocean surface from its mean level, and is the acoustic grazing angle. In the case where,thesurface roughness is small scale and the main part of the scattered energy propagates in the specular direction as a coherent wave with intensity equals to the product,where is mean scattered pressure. For large sea surface roughness, the coherent component is close to zero and the scattered field is almost completely incoherent [1]. Various studies have examined the effects of sea surface roughness. Early works on scattering at rough sea surface were discussed in a literature survey carried out by Fortuin [2]. Two widely known theoretical methods for calculating acoustic scattering from rough surfaces are the Rayleigh Rice and Kirchhoff approximations [3], [4]. Each approach applies to acoustic scattering from rough surfaces of different scale. Rayleigh Rice method is based on the small roughness perturbation approximation and is limited by roughness with small heights and slopes. The Kirchhoff method is based on the physical optics approximation and is limited to gently undulating surfaces or smooth roughness (although large). McDaniel and McCammon [5] combined both methods to model scattering from a multiscale rough sea surface. They used the root-mean-square (rms) surface heights and slopes predicted by an empirical surface wave model as parameters for calculating the intensity of acoustic forward scatter. Thorsos [6] also took the approach of using an empirical surface wave model to examine the accuracy and validity of the Rayleigh Rice and Kirchhoff approximations for low-frequency acoustic scattering from sea surfaces through comparison with exact integral equation results. Instead of only using surface wave statistics such as rms wave heights and slopes, the model used actual rough surface realizations as inputs. Dahl [7] conducted two experiments to observe the time and angle characteristics of high-frequency sound which was scattered from rough sea surface. The Kirchhoff approximation method was then used to interpret the results and to obtain simple relationships between geometry of acoustical scattering, surface wave conditions, and time-angle spreading of the received signals. Acoustic propagation models consist of two separate classes: 1) full wave models and 2) ray-based models. When the processing speed is essential, ray-based models are common choice for modeling acoustic propagation [8]. A coupled 1-D empirical surface model with an acoustic Gaussian beam tracing model /$ IEEE

2 2 IEEE JOURNAL OF OCEANIC ENGINEERING Bellhop [9] was developed [10], [11]. In that study, surface realizations were uncorrelated since for each run of Bellhop, different random realizations of the surface were generated. A Monte Carlo procedure was used to calculate the standard deviation of arrival time and arrival angle. In comparison, the present study combines the acoustic model Bellhop with a realistic, time-evolving sea surface model [12], [13] to simulate the fluctuations of arrival times and arrival angles observed in shallow-water acoustic transmissions. This 2-D approach does not directly address the out-of-plane scattering caused by surface waves; to properly model these out-of-plane scattering effects, a full 3-D acoustic wave model may be required. Instead, the present 2-D acoustic model provides a simple and computationally efficient technique of examining the fluctuations of arrival times and angles caused by surface waves. A High-Frequency Acoustic Experiment (HFA97) was conducted on September 22 29, 1997 in a shallow-water region of the Delaware Bay [14]. During the experiment, acoustic signals were transmitted between source receiver tripods deployed on the seafloor, while highly calibrated environmental data were collected simultaneously at a nearby oceanographic observation platform [15]. Source receiver tripods were carefully spaced in range so rays with a single surface interaction were easily distinguished in received signals. Extensive analysis of the single surface reflected portion of received signals shows correlation between signal fluctuations and wind speed [14] providing information on the relationship between acoustic transmissions and sea surface variability. The HFA97 data set is used to guide model development and to validate the results. The focus of this paper is to present a combined water wave and acoustic wave model to predict acoustic signal temporal fluctuations induced by a sea surface boundary. Comparisons between this simple model output and experimental observations are presented to show the feasibility of the approach and indicate the range of model validity. In Section II, a brief description of the experimental data and some observations are presented. In Section III, the selected acoustic and ocean surface models are introduced along with a description of how the two models are integrated. An approach used in this study to achieve high resolution and more accurate results while maintaining computational efficiency of a ray-based model is discussed in this section. The effect of sea surface resolution on the accuracy of the results is also discussed in this section. Section IV shows comparisons between model output and experimental observations. In Section V, some brief concluding remarks are made along with suggestions for future work. II. EXPERIMENTAL DATA The HFA97 experiment was conducted in a central region of the Delaware Bay at W and N. Two bottom mounted tripods, each having an acoustic source and three receiving hydrophones, were placed in 15 m of water depth and separated by 387 m. On each tripod, the source was located m above the seafloor and the three receiving hydrophones were located at 0.33, 1.33, and 2.18 m above the seafloor, respectively (see Fig. 1). The sources transmitted reciprocal broadband chirp signals over the frequency range of 1 18 khz. Fig. 1. HFA97 experiment setup. There are two types of signals observed in the data, those resulting from overhead transmission (dashed lines above tripod A) and those resulting from remote transmission (solid lines between tripods A and B). Group I consists of direct and bottom reflected rays. Group II consists of SSR rays number 2 to number 5. Fig. 2. Overhead transmission arrival time versus geotime for a 40-s transmission period: (a) during low wind speed ( m/s) and (b) during high wind speed (13.9 m/s). In (b) up and down fluctuations of arrival time across 40-s period indicate surface height fluctuations. During the experiment, two different pulse transmission rates were used so as to capture the slow and fast temporal variations of the acoustic field driven by different physical ocean processes. In the first case, a broadband chirp signal was transmitted every s for a 5-s duration and repeated every 10 min for the entire experiment which lasted about a week. In the second case, the same chirp signal was transmitted every s for a 40-s duration and then repeated every hour for the entire experiment. In both sampling cases, each received signal has sufficient time to clear from any scattered signals before the next signal arrives so that overlapping does not occur. In this paper, individual s transmissions are referred to as pings. For this particular study, analysis focuses on two types of received signals. The first type are those received on the first tripod s highest hydrophone (i.e., 2.18 m above the seafloor) resulting from signals transmitted from the source on the same

3 KARJADI et al.: THE EFFECTS OF SURFACE GRAVITY WAVES ON HIGH-FREQUENCY ACOUSTIC PROPAGATION IN SHALLOW WATER 3 Fig. 3. Surface wave spectra and received acoustic signals arrival time from September 24, 1997 at 00:00:00 L to September 25, 1997 at 00:00:00 L. (a) Wind speed and wind direction. (b) Overhead transmission estimation of spectrum. (c) Signal amplitude versus arrival time for geotimes separated by 10-min intervals. Group I consists of direct and bottom reflected rays. Group II consists of SSR rays. Group III consists of two-surface-reflected rays. Group IV consists of threesurface-reflected rays. tripod. These signals are referred to as overhead transmission since they involve acoustic waves that travel from the source up to the sea surface and back down to the tripod after one sea surface reflection (path is shown by vertical dashed lines in Fig. 1). Plots of two different 40-s overhead transmissions are shown in Fig. 2 for a calm period [wind speed 1 m/s; Fig. 2(a)] and for a rough period [wind speed of 13.9 m/s; Fig. 2(b)]. In Fig. 2(b), fluctuations in arrival time indicate surface height fluctuations caused by wind generated surface waves. The second type of received signals observed in HFA97 data result from acoustic waves traveling from the source on one tripod to the three remotely mounted hydrophone receivers, located 387 m away on the opposite tripod (paths are shown by solid lines from tripod A to tripod B in Fig. 1). These are referred to as remotely received signals. Group I consists of direct and single bottom reflected paths while Group II consists of single surface reflected (SSR) ray paths. Ray number 2 is surface only bounce, number 3 is bottom-surface bounce, number 4 is surface bottom bounce, and number 5 is bottom surface bottom bounce. For these signals, the HFA97 experimental design allowed for examination of the time evolution of individual ray paths of SSR rays. This paper focuses on ray number 2 only. Although no direct surface wave measurements were taken during the HFA97 experiment, overhead transmission signals received on the first tripod s highest hydrophone can be used to obtain information about sea surface fluctuations. Average sea surface height and sound-speed measurements were used to convert arrival time of single surface reflected overhead signals (example in Fig. 2) to surface fluctuations. For each 40-s transmission time, individual pings were used to estimate sea surface heights at s interval. The resulting 40-s time series of the sea surface heights were used to calculate the surface wave frequency spectrum at different 40-s transmission geotimes. Fig. 3 shows the sea surface frequency spectra calculated using the acoustic overhead method described above together with the measured wind speed and directionfora24-hperiod from September 24, 1997 at 00:00:00 L to September 25, 1997 at 00:00:00 L. The figure shows that spectral level increases with wind speed. Example of comparison with the JOint North Sea WAve Project (JONSWAP) [16] spectrum for wind speed of 13.4 m/s is given in Fig. 5(c). In this experiment, typically when the wind speed is 10 m/s, the rms surface heights obtained from acoustic overhead transmissions are smaller than those predicted by the JONSWAP spectra. This is consistent with a more elaborate study of wave prediction using the Simulating WAves Nearshore (SWAN) [17] model, which also gives surface height estimates that greatly exceed the acoustical estimates at higher wind speeds [18]. We suspect that the dropoff in the acoustical estimates versus established model estimates is due to obscuring of the surface return due to bubbles in the water column after the onset of whitecapping, but more efforts on comparing the acoustic overhead method with real ocean wave measurements are required to determine its accuracy. Fig. 3 also shows the arrival time of received acoustic signals for four groups of arrival. In addition to Groups I and II mentioned above, Group III consists of rays with two surface reflections and Group IV consists of rays with three surface reflections. During low wind speeds, the signals are distinct and stable while at higher wind speeds the rays break up into smaller peaks resulting from the generation of micro multipaths. In previous HFA97 analysis, remotely received signals across the three hydrophones were used with a beamforming technique to calculate signal arrival angle as a function of arrival time [14]. By considering the geometry of the HFA97 experimental setup (Fig. 1), the resulting beamformed plots can be used to

4 4 IEEE JOURNAL OF OCEANIC ENGINEERING intensive compared to full-wave acoustic models while still providing satisfying results. The conventional ray modeling implementations have shortcomings (two common ray tracing anomalies happen where the shadow zones and caustics occur). To overcome these, there have been a number of efforts proposed to improve the results but retain computational efficiency. One such method is Gaussian beam tracing [9]. With this technique a fan of rays is traced from a point source with trajectories governed by the standard ray equations. The Gaussian beam method associates with each ray a beam with a Gaussian intensity profile normal to the ray. An additional set of equations which governs beam width and curvature is integrated along with the standard ray equations. The Gaussian beam tracing method has been adapted to the typical ocean acoustics waveguide and has been implemented as a tool called Bellhop [9]. This model has been rigorously tested and the results show excellent agreement with certain full wave models at high frequencies [19]. The method very much mitigates the numerical artifacts affecting standard ray models and still retains the computational efficiency of a ray-based approach. B. Ocean Surface Waves Fig. 4. Remotely received signal arrival angle versus arrival time for calm (wind speed 2 m/s), intermediate (wind speed 5 m/s), and rough (wind speed 13 m/s) periods. For calm period SSR ray paths are easily distinguished in the signal (numbers correspond to ray paths labeled in Fig. 1). The ray paths become more difficult to distinguish for more rough conditions. distinguish the portion of the received signal corresponding to SSR ray paths (Fig. 4). For calm surface condition ray paths are easily distinguished in the signal (numbers correspond to ray paths labeled in Fig. 1), then they become more difficult to distinguish for rougher conditions. Since this experiment was aimed at measuring cause and effect between the ocean environment and acoustic propagation, several oceanographic and meteorological measurements were made simultaneously with acoustic measurements. Oceanographic measurements included tide height, current, temperature, and salinity profiles while meteorological measurements included air temperature, wind speed, and wind direction. For this study, wind speed and direction measurements will be used to construct the initial sea surface wave fields. III. MODELING METHODS A. Ray Theory and Gaussian Beam Tracing Acoustic ray methods are attractive for high-frequency modeling problems because they are very much less computationally In this study, the surface wave is generated by a 2-D linear time-evolving surface model following the approach given by Dommermuth and Yue [12]. There were no direct measurements of sea surface wave spectrum in the HFA97 experiment. Therefore, in this study of a fetch-limited coastal area, the JON- SWAP [16] spectrum is used for construction of initial wave fields. JONSWAP spectrum provides a relationship between wind speed and fetch length with the frequency spectrum. After the construction of the initial wave field specified by the JONSWAP spectrum, the wave evolution equations are solved numerically to simulate the surface wave realizations. The corresponding 1-D cross sections of the 2-D surface realizations in the direction of the acoustic track are then used as sea surface boundaries in Bellhop. 1) JONSWAP Frequency Spectrum: Thereareanumber of empirically derived surface wave models available in the form of surface wave height frequency spectra. A surface wave frequency spectrum represents the distribution of wave energy across a range of frequencies and describes the total energy transmitted by a wave field at a given time. Wave spectra are strongly influenced by the wave-producing wind and its temporal/spatial characteristics. The spatial variability of wave spectrum is primarily encapsulated into the effect of fetch which is the length of the sea surface over which the wind blows to generate waves. In coastal regions, the wind acts on a limited fetch. As a result, the sea will not become fully developed and the large-scale or swell components of the waves will be significantly reduced in amplitude. The JONSWAP spectral model computes a sea surface frequency spectrum under fetch-limited conditions as function of wind speed [16]. This model is based on an extensive wave measurement program (Joint North Sea Wave Project) carried out in 1968 and 1969 in the North Sea. In this study, the JONSWAP spectrum is used to construct the initial wave field

5 KARJADI et al.: THE EFFECTS OF SURFACE GRAVITY WAVES ON HIGH-FREQUENCY ACOUSTIC PROPAGATION IN SHALLOW WATER 5 for the surface model. The fetch length for Delaware Bay area varies between 13 and 22 km depending on wind directions. The JONSWAP spectral model takes the form (1) To construct an initial water surface, the directional wave spectrum needs to be transformed to a wave number spectrum,where and are wave number components along -and -axes, respectively. Considering energy equality under surfaces of and leads to where is the angular frequency, is the gravitational acceleration, and is a peak enhancement factor given by (2) where (11) is the Jacobian of the transformation and is given by (12) The parameters and are given as for,and for, while is a function of fetch length, and wind speed, and peak frequency is given as A wave number spectrum can be obtained from the frequency spectrum considering the energy equality under both curves which leads to where is the wave number of ocean waves. The relationship between and is given by gravity wave dispersion relationship from which the expression for group velocity (3) (4) (5) (6) can be derived (7) interval can be ob- The amplitude spectrum for each tained by energy equality (13) where and are indexing values from 0 to and, respectively. The amplitude spectrum is then mirrored about and to produce by amplitude spectrum. A phase grid is generated using uniformly random phases with values between 0 and. Complex amplitude is generated in wave number space as (14) A 2-D initial water surface at each of by grid point can be obtained by taking 2-D Fourier transforms of.the surface partitions and must be selected carefully and will be discussed in Section III-C. An initial surface velocity potential is similarly constructed. Details of the computation can be found in [13]. 3) Wave Model: The classical kinematic and dynamic boundary conditions at the free surface in terms of surface velocity potential,where, are given by [12], [13] (15) 2) Constructing Initial 2-D Surface Wave Realizations: In a 2-D wave field, we need to consider directional wave spectra given by where is the directional spreading function given by [20] (8) (9) (16) where is the horizontal gradient, is time, is the gravitational acceleration, is atmospheric pressure, is water density, and is water surface fluctuation from the still water level. In the case of linear surface waves used in this paper, (15) and (16) reduce to where is the mean wave direction and (17) (18) otherwise. (10) evaluated at. Starting with initial wave field and, time stepping in (17) and (18) is accomplished using a fourth-order Runge Kutta integrator with a constant time step [12].

6 6 IEEE JOURNAL OF OCEANIC ENGINEERING Fig. 5. Example of sea surface realizations generated by the 2-D time-evolving sea surface model. (a) Snapshot of a 2-D wave field. Waves come from the North (0 wind direction). (b) Corresponding 1-D cross section of sea surface realizations in the direction of acoustic tracks A to B. (c) JONSWAP frequency spectrum with wind speed 13.4 m/s and fetch length of 22 km used to construct the initial wave field (solid line) and spectrum obtained from overhead acoustic transmission (dashed line). In the case of nonlinear surface waves, following Dommermuth and Yue [12], the nonlinear evolution equations for and are given by (15) and (16) while the surface vertical velocity is expressed as (19) where are the eigenfunctions representing the expansion of where is the number of eigenmodes, and where is the expansion order of wave steepness. The numerical method used for solving the evolution equations is a two-step procedure [12]. First, given the initial wave field and, all spatial derivatives are evaluated in wave number space while nonlinear products are calculated in physical space. Second, time integration is accomplished using a fourth-order Runge Kutta time integrator. Starting from initial conditions, this two-step procedure is repeated for every time step. Further details of the wave model can be found in [13]. C. Integration of Bellhop and Surface Model Empirical sea surface models have been combined with acoustic models in past studies of similar nature [5], [6], [21] and field data have been used to guide development of such models. A model which includes out-of-plane scattering has recently been developed and compared with field data [7], [22] [24]. Their results show that out-of-plane scattering depends on the value of grazing angle. For single surface bounce with small grazing angle, the out-of-plane scattering is relatively small compared to the in-plane scattering [7], [23], [24]. Accordingly, the 2-D acoustic model discussed in the present Fig. 6. Sketch of a small ray fan used in the model to achieve higher resolution while maintaining computational efficiency of the ray-based model. The star indicates the specular point. Rays with takeoff angles within insonify, length of surface within several surface wavelengths from the specular point. paper assumes that the out-of-plane scattering of the acoustic field is negligible for the surface-only reflected rays. The modeling approach presented here however is unique in terms of using a realistic surface realization to simulate the effects of rough sea surface with computational efficiency of a ray-based model. The concept behind this combined sea surface/acoustic model is the utilization of a 2-D time-evolving rough ocean surface realization and the Gaussian beam tracing model (i.e., Bellhop). The initial wave field is constructed using HFA97 wind speed measurements and the JONSWAP wave number spectrum. The corresponding evolving 1-D cross section of surface realizations in the direction of the acoustic track are then read into Bellhop as (horizontal range, surface height) points with surface partition width and become the upper boundary over the water column through which beams are traced.

7 KARJADI et al.: THE EFFECTS OF SURFACE GRAVITY WAVES ON HIGH-FREQUENCY ACOUSTIC PROPAGATION IN SHALLOW WATER 7 Fig. 7. Example of model run results for wind speed 7 m/s with uniform sound speed over the water column. (a) Eigenrays plot. The stars are source and receiver, and open circle on the water surface is the specular point. is the vertical distance from the receiver and dashed-line rays are those reflected from the surface more than once. (b) Closeup plot near the surface. (c) plot of pair of eigenrays versus takeoff angles, where is the vertical distance from the receiver. For real eigenrays, is equal to zero. (d) Midpoint iteration to get the real eigenray whose. Fig. 5 shows an example of the JONSWAP wave spectrum for constructing the initial wave field, snapshots of a 2-D wave field, and the corresponding 1-D cross section of surface realizations. When a beam interacts with the rough surface boundary, the beam trajectory is geometrically reflected from the surface, depending on the surface slope at the point of intersection and the beam s angle of incidence. The resulting model output simulates the fluctuations in arrival time and arrival angle observed in the HFA97 transmissions. For the HFA97 case, using the center frequency of the signal (12 khz), the typical for the Delaware Bay region ( m), and 3.6, the surface roughness (Rayleigh) parameter, which indicates that the SSR portion of received signals consists of mostly incoherent scattering (on an ensemble mean basis). This combination of high-frequency and large-scale roughness justifies the approach of geometrically reflecting acoustic ray paths from individual points on the rough ocean surface [22]. 1) Approach for Higher Resolution and Accuracy: Fig. 6 illustrates the approach used in this study to achieve higher resolution in the model while maintaining computational speed. Since we only consider the single surface-only reflected rays (ray path 2 in Fig. 1), then instead of using a large range of ray takeoff angles to cover a large portion of the surface, we need only to consider a smaller range, which insonifies part of the surface within several surface wavelengths from the specular point. Hence, with the same number of rays, as with larger range of takeoff angle, model resolution is increased while maintaining the same computational time. For a rough surface, instead of giving eigenrays which go through the receiver, typically Bellhop will give pairs of eigenrays where the receiver lies between the eigenrays in the pair. To obtain eigenrays which go through the receiver, we perform a midpoint iteration for each eigenrays pair. Fig. 7 shows an example of model results for a run with random surface realization generated by 7-m/s wind and Delaware Bay average fetch of 10 nautical miles. The sound speed was assumed uniform in depth. Fig. 7(b) is the closeup plot near the surface where the circle is the specular point for flat surface. Eigenrays shown in dashed lines are those reflected from the surface more than once. We disregard these rays because they usually are much farther away from the receiver. Fig. 7(c) shows values of for the eigenrays, where is defined as the vertical distance from the receiver [see Fig. 7(a)]. For real eigenray, is equal to zero. In this particular example, Bellhop gives 9 pairs of eigenrays as shown in Fig. 7(c), and a midpoint iteration was performed to obtain the corresponding 9 real eigenrays [Fig. 7(d)]. 2) Effects of Sea Surface Resolution: When generating a surface realization, surface partition width must be selected carefully. In previous studies that have involved generating surface realization using the spectral method, setting this length has remained an unresolved problem of particular interest [6]. Intuitively, sea surface with more details will better represent the surface realization, but need to be constructed with a smaller, and hence at the cost of higher computational time. The model s results show that the number of eigenray pairs increases with the number of surface partition.asanexample, Fig. 8 shows results for a case where the surface was generated by 7-m/s wind resulting in peak period of about 3 s and corresponding wavelength of about 15 m. Here the number of eigenray pairs for one instant time step are 9, 7, and 4 for

8 8 IEEE JOURNAL OF OCEANIC ENGINEERING Fig. 8. Comparisons of model results with different size of surface partitioning. Examples of model run results for wind speed 7 m/s with uniform sound speed over the water column: (a) ( 0.4 m), (b) ( 1.5m),and(c) ( 6.1 m). Top panels are plots of eigenrays, middle panels are the closeup plots near the surface, and bottom panels are the plots of eigenray pairs as output of the model.,and, respectively, confirming that higher number of is required to capture all the eigenrays. Note that the surface partition of equalto64( 6.1 m) is about one half of the peak wavelength and clearly does not represent the sea surface. Fig. 9 plots the standard deviation of arrival time as a function of wind speed for different values of where the straight lines represent their linear fits for each.thisfigure shows that the lines converge for large values of, thus confirming the requirement of using higher resolution of surface partition to obtain higher accuracy. The convergence also confirms that there is an optimal number of surface partition,whichrelates to computational cost and accuracy. IV. MODEL RESULTS The results shown hereafter involve the modeling of remotely received signals sent over the distance of 387 m between the two tripods. To assess the accuracy of model results, time-angle fluctuations of single surface-only reflected beams (ray path 2 in Fig. 1) were measured in the HFA97 data. Time-angle standard deviations for the first SSR were calculated for each hourly, 40-s transmission consisting of 115 chirp signals. Beamformed plots (Fig. 4) were used to pick out the portion of the received signals that correspond to a specific raypath. Fig. 4(a) represents a signal that was transmitted during a calm period (wind speed 2 m/s) and four individual SSR ray paths can be clearly distinguished. In similar plots for rougher periods [Fig. 4(b) and (c)], it becomes more difficult to distinguish between four individual SSR rays due to the breakup and formation of micro multipaths resulting in incoherent scattering at the Fig. 9. Standard deviation of arrival time as a function of wind speed for different sea surface partitioning ( and ). rough sea surface. For most rough and calm period plots however, it is feasible to pick out the very first arriving SSR ray path in the Group II arrival. Beamformed results were then used to track time-angle fluctuations of the first SSR arrivals in the HFA97 data. Time-angle standard deviations of the first SSR were calculated for the group of 115 signals received during each hourly 40-s transmission interval for 19 h from September 24, 1997 at 05:00:00 L to September 25, 1997 at 00:00:00 L. Time-angle standard deviations are then plotted against the wind speed recorded at that transmission time (see Fig. 3). There was significant variation in weather conditions during the HFA97 experiment,

9 KARJADI et al.: THE EFFECTS OF SURFACE GRAVITY WAVES ON HIGH-FREQUENCY ACOUSTIC PROPAGATION IN SHALLOW WATER 9 Fig. 10. Model data comparison of standard deviation of arrival time and arrival angle as a function of wind speed. Triangles and stars are data and model results, respectively. Dashed lines are linear fit of the values. so time-angle standard deviation values are available for a broad range of wind speeds. Similarly, we ran the model based on 24-h data of wind, tides, and sound-speed profile from September 24, 1997 at 00:00:00 L to September 25, 1997 at 00:00:00 L. At each hour, the surface model was run with for 40 s and every s the surface realizations were recorded and used as sea surface boundary input to Bellhop. For each realization, a midpoint iteration was performed to get the real eigenrays. Then, arrival time for each realization was defined as the minimum arrival time among these eigenrays. As a result, at each hour, there were 115 realizations resulting in 115 arrival times and corresponding arrival angles. To compare model result with data, Fig. 10 plots the standard deviation of arrival time and arrival angle as a function of wind speed for both model and data. Data show that arrival time and arrival angle fluctuations increase as wind speed increases, which is also predicted by the model. Notice that there is a large spread in the data, especially during high wind speeds. The model underestimates thefluctuation of arrival time especially during high wind speeds, suggesting that there are physical processes which need to be included in the model, such as bubbles and turbulence effects as well as 3-D or out-of-plane scattering. V. CONCLUSION Combining a time-evolving sea surface model and a ray-based acoustic model presents an efficient approach to predicting fluctuations in acoustic signals induced by sea surface roughness. Tracing beams through sea surface fluctuations and changing beam direction at surface reflection based on surface slope result in a realistic simulation of time-angle fluctuations in received signal. Also, using ray-based acoustic methods makes the model computationally efficient since multiple model runs can be made quickly supporting timely model modification and improvement. Initial comparisons between this combined model output and HFA97 observations yield good results and suggest that there are other physical processes that need to be included in the model, such as bubble effects. Data from other high-frequency shallow-water acoustic experiments will be compared with the model for further validation of this approach. Also, subsequent work will focus on using this modeling approach to predict amplitude fluctuations of acoustic signals induced by sea surface roughness. The wave model provides velocity components in the normal direction to the surface, thus calculations of Doppler frequency shift due to sea surface motion can be performed as well. Extending the surface wave model to a nonlinear model to simulate wave breaking and to locate bubbles population in the wave field would appreciably improve the combined acousticwave model. Ultimately extending to a 3-D model that includes out-of-plane scattering would be the accurate way to simulate the effects of sea surface roughness on the acoustic propagation. ACKNOWLEDGMENT The authors would like to thank all participants of the HFA97 and HFA2000 experiments particularly S. Forsythe, L. Lenain, R. Heitsenrether, and J. Luo for their help in various aspects of the program from 1997 through They would also like to thank M. Porter for providing help with Bellhop model and for discussions on the project. REFERENCES [1] L. Brekhovskikh and Y. Lysanov, Fundamentals of Ocean Acoustics, 3rd ed. New York: Springer-Verlag, 2003, pp [2] L. Fortuin, Survey of literature on reflection and scattering of sound waves at the sea surface, J.Acoust.Soc.Amer., vol. 47, pp , [3] E. I. Thorsos, The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum, J. Acoust. Soc. Amer., vol. 83, pp , [4] J. A. Ogilvy, TheoryofWave Scattering From Random Rough Surfaces. London, U.K.: IOP, 1991, ch [5] S.T.McDanielandD.F.McCammon, Composite-roughness theory applied to scattering from fetch limited seas, J. Acoust. Soc. Amer., vol. 82, pp , [6]E.I.Thorsos, Acousticscattering from a Pierson-Moskowitz sea surface, J. Acoust. Soc. Amer., vol. 88, pp , [7] P. H. Dahl, High-frequency forward scattering from the sea surface: The characteristic scales of time and angle spreading, IEEE J. Ocean. Eng., vol.26,no.1,pp , Jan [8] K.L.Williams,E.I.Thorsos, and W. T. Elam, Examination of coherent surface reflection coefficient (CSRC) approximations in shallow water propagation, J. Acoust. Soc. Amer., vol. 116, pp , 2004.

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Hui, Directional spectra of wind generated waves, Phil. Trans. Roy. Soc. Lond. A, vol. 315, pp , [21] M. Siderius and M. B. Porter, Modeling broadband ocean acoustic transmissions with time-varying sea surface, J. Acoust. Soc. Amer., vol. 124, pp , [22] P. H. Dahl, On the spatial coherence and angular spreading of sound forward scattered from the sea surface: Measurements and interpretive model, J. Acoust. Soc. Amer., vol. 100, pp , [23] P. H. Dahl, On bistatic sea surface scattering: Field measurements and modeling, J. Acoust. Soc. Amer., vol. 105, pp , [24] J. W. Choi and P. H. Dahl, Measurement and simulation of the channel intensity impulse response for a site in the east China sea, J. Acoust. Soc. Amer., vol. 116, pp , Entin A. Karjadi received the B.S. degree in civil engineering from Bandung Institute of Technology, Bandung, Indonesia, in 1984 and the M.C.E. and Ph.D. degrees in civil engineering from University of Delaware, Newark, in 1991 and 1997, respectively. She was a faculty member at the Ocean Engineering Program, Bandung Institute of Technology, from 1984 to 1986 and from 2001 to From 1997 to 1999, she was a Postdoctoral Fellow at the Center for Applied Coastal Research, University of Delaware. In 2006, she joined the Ocean Acoustic Laboratory, University of Delaware as a Postdoctoral Researcher. Her research interests are ocean surface wave and acoustic propagation in shallow water. Mohsen Badiey (M 94) received the Ph.D. degree in applied marine physics and ocean engineering from the Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL, in He was a Postdoctoral Fellow at the Port and Harbour Institute, Ministry of Transport, Tokyo, Japan, from 1988 through 1990, and worked on research problems related to the water wave interaction with seafloor and on seismic wave propagation in continental shelf regions. In 1990, he became a faculty member at the College of Earth, Ocean, and Environment, University of Delaware, Newark, where he presently is a full Professor in the Physical Ocean Science and Engineering Program and in Civil Engineering Department. From 1992 to 1995, he managed the ocean acoustics program at the Office of Naval Research. His research interests are physics of sound and vibration, underwater acoustics in shallow-water regions, acoustical oceanography, underwater acoustic communications, seabed acoustics, and geophysics. Dr. Badiey is a Fellow of the Acoustical Society of America. James T. Kirby received the B.Sc. and M.Sc. degrees in engineering mechanics from Brown University, Providence, RI, in 1975 and 1976, respectively, and the Ph.D. in civil engineering from University of Delaware, Newark, in He worked as a Research Engineer at Alden Research Laboratory, Holden, MA, from 1977 to He has subsequently been employed with the Marine Sciences Research Center, State University of New York at Stony Brook ( ), Coastal and Oceanographic Engineering Department, University of Florida ( ), and the Civil and Environmental Engineering Department, University of Delaware (1989-present). He is presently the Edward C. Davis Professor of Civil and Environmental Engineering, and holds a joint appointment in the College of Earth, Ocean, and Environment. His principal research areas are ocean surface wave mechanics, near-shore hydrodynamic and sedimentary processes, and tsunamis. Dr. Kirby is a member of the American Geophysical Union, the American Society of Civil Engineers, and the American Physical Society. He is former Editor-in-Chief of the ASCE Journal of Waterway, Port, Coastal and Ocean Engineering and the AGU Journal of Geophysical Research Oceans. He presently serves on the Board of Governors for the American Institute of Physics. Cihan Bayındır (S 11) received the B.S. degree, with honors rank, in civil engineering from the Boǧaziçi University, İstanbul, Turkey, in 2007, the M.S. degree in coastal and ocean engineering with a minor in mathematics from the University of Delaware, Newark, in 2009, and the M.S. degree in electrical and computer engineering with minors in mathematics and mechanical engineering from the Georgia Institute of Technology, Atlanta, in 2011, where he is currently working towards the Ph.D. degree at the Department of Civil and Environmental Engineering. He completed his Ph.D. minor studies in electrical and computer engineering with an emphasis on synthetic aperture radar imaging. He was a Research Assistant for an underwater acoustics project supported by the Office of Naval Research at the University of Delaware. His research interests are synthetic aperture radar and sonar imaging, underwater acoustics, fluid mechanics, computational mathematics, and parallel programming in general. Mr. Bayındır is a member of the IEEE Oceanic Engineering Society.