1 Introduction

Effects of the real sea surface on sound scattering and reflection have attracted the scientists’ attentions for quite a long time. This is primarily due to the wide variety of sound applications in the underwater environment. For instance, underwater communication channels(van Walree, 2013; Huang et al., 2013; Jornet et al., 2010; Yerramalli and Mitra, 2011; Polprasert et al., 2011), evaluation of sonar performance(Porter, 1993), marine life(Diachok, 1999), scattering of underwater sound sources from the sea surafece(Ghadimi et al., 2014), and oceanography(Holliday et al., 1995)are some of the most important subjects in underwater acoustics related to sea surface effects. In most of these subjects, it is required to provide an appropriate acoustic model in order to include sea surface effects on the entering sound. These effects are due to various phenomena, which were studied by many investigators. Doppler effects(Eggen et al., 2000; Sharif et al., 2000), attenuation and absorption(van Moll et al., 2009), bubble population and effects(Farmer et al., 2001; Deane et al., 2013; Ainslie, 2005; Duro et al., 2011), sound transmission(Godin, 2008a, b; Calvo et al., 2013), sound propagation in shallow waters(Yang, 2012; Roux et al., 2010; Song et al., 2010) and surface waves(Karjadi et al., 2012; Dol et al., 2013)can be considered as important phenomena at the sea surface.

In order to present a precise modeling of the sea surface, many investigations have been conducted since World War II. In fact, a comprehensive view of sound propagation was essential for many applications such as underwater sound communication, detection and anti-submarine warfare(ASW)operations. Developments in this field have been achieved by both marine seismologists and underwater acousticians, even though the motivating factors have been different. Marine seismologists have traditionally applied earthborn propagation of elastic waves in order to examine the solid earth below the oceans. On the other h and, underwater acousticians have focused on the study of waterborne, compression-wave propagation phenomena in the ocean as well as in the shallow sub-bottom layers(Akal and Berkson, 1986).

Propagation models have continued to be used for prediction of sonar performance. They have also been found as great utilities in analyzing the field measurements, designing the improved sonar systems, and designing the complicated inverse-acoustic field experiments. However, in order to achieve these goals, various aspects of propagation phenomena such as ducts and channels, boundary interactions, and volumetric influences should be studied among which sea surface boundary conditions are particularly interesting. Accordingly, effects of sea surface boundary on sound propagation are studied in this paper. Sea surface affects the underwater sound by providing a mechanism(Etter, 2003)for:

1)Forward scattering and reflection loss;

2)Image interference and frequency effects;

3)Attenuation by turbidity and bubbles;

4)Noise generation at higher frequencies due to surface weather; and

5)Backscattering and surface reverberation.

The resulted values of the mechanisms operating at the sea surface can be incorporated into mathematical models through the specification of appropriate “boundary conditions”. These boundary conditions can range from a simplistic form to a complex form depending on the sophistication of the model and availability of the required information concerning the state of the sea surface.

When a plane sound wave in water strikes a perfectly smooth surface, nearly all of the energy is reflected at the boundary in the forward direction as a coherent plane wave(Etter, 2003). Since the sea surface roughness is under the influence of wind, sound is scattered in the backward and out-of-plane directions and the intensity of sound reflected in the forward direction is accordingly reduced. The backward-directed(back scattered)energy gives rise to the surface reverberation(Etter, 2003). Eckart(1953) developed a theoretical method of scattering by a sinusoidal boundary as a way to approximate reflection from a wind-roughened sea surface. Marsh(1961) developed simple formulae to determine scattering losses at the sea surface. Eller(1984) reviewed the availability of simple surface loss algorithms appropriate for being applied to the propagation models.

The sea surface is most commonly modeled as a pressure release surface(Kinsler et al., 1982). This is a condition in which the acoustic pressure at the air-water interface is nearly zero. The amplitude of the reflected wave(in water)is approximately equal to that of the incident wave, albeit there is an 180º phase shift. This is also known as the Dirichlet boundary condition(Frisk, 1994). It is also a common practice to use the term “reflection coefficient” signed by ℛ in order to express the amount of acoustic energy reflected from a surface or from a boundary between two media. This coefficient depends on the grazing angle and the difference in the acoustic impedance between the two media. A reflection loss is then defined as 10log₁₀ℛ.

Sea-surface wave spectra can be generated numerically by executing available spectral ocean wave models in the hindcast mode(Etter, 2003). Hindcasting is usually the only means available for obtaining sufficiently long record lengths from which reliable statistics is generated. A statistical analysis of these hindcast data results in probability distributions of critical parameters for using in estimation of future sea-surface conditions. Kuo(1988) reviewed and clarified earlier formulation related to sea-surface scattering losses based on perturbation methods and also presented new predictions based on numerical integration in a complex domain. The perturbation method has been known to be quite accurate for estimating low-frequency acoustic wave scattering loss among theoretical approaches(Kuo, 1988).

In a real sea condition, sea surface roughness and presence of subsurface bubble clouds are essential factors, which are needed to be taken into account in order to accurately study the sea surface boundary. When the sea surface is rough, the vertical motion of the surface modulates the amplitude of the incident wave and superposes its own spectrum as upper and lower side b and s on the spectrum of the incident sound(Urick, 1979). In addition, when there is a surface current, the horizontal motion will appear in the scattered sound and cause a Doppler-shifted and Doppler-smeared spectrum(Etter, 2003). Also, the presence of bubble layers near the sea surface further complicates the reflection and scattering of sound as a result of the change in sound speed, the resonant characteristics of bubbles and the scattering by bubbly layers(Leighton, 1994).

Hall(1989) developed a comprehensive model for the wind-generated bubbles in the ocean and examined the resulting effects on the transmission of short pulses in the frequency range of 1.25-40 kHz. Hall also concluded that for long-range propagation, the decrease in the near-surface sound speed due to bubbles cannot result in variation of the surface-reflected ray intensity.

In addition to different theoretical approaches in this area of study, various field experiments have been conducted in order to examine sea surface boundary conditions in sound propagation. One such experiment was conducted by Urick and Hoover(1956). By using two transducers(one for transmitting and one for receiving), they measured backscattering of sound pulses from the surface of the sea as a function of grazing angle between 5º and 90º, wind speed between 3 and 18 knots, and pulse length.

A series of measurements conducted by Chapman and Harris(1962) were analyzed in octave b and s between 0.4 and 6.4 kHz and the results were expressed by the empirical relations. Chapman and Scott(1964) later verified these results over the frequency range of 0.1-6.4 kHz for grazing angle below 80º. Works of Brown and Saenger(1972) and Andreeva et al.(1980) are other examples of experimental study of surface scattering. McDaniel(1993) reviewed his recent advances in the physical modeling of monostatic sea-surface reverberation in the frequency range of 200 Hz-60 kHz(also see the extensive review by Fortuin(1970). For his review, he considered three sources of surface reverberation: rough-surface scattering, scattering from resonant bubbles and scattering from bubble clouds(or plumes).

Ogden and Erskine(1994a) mentioned that most of these measurements had been limited in the amount of data collected, the grazing angle or frequency range or the environmental conditions encountered. They did extensive measurements of low-frequency(70-1000 Hz)sea surface backscattering strengths as part of the Critical Sea Test(CST)experiments which is known as the most complete study in sea surface effects on sound propagation up to today. In CST experiments, measurements of low-frequency(70-1000 Hz)sea surface backscattering strengths were done. These measurements were made during CST-1 through CST-7 for a variety of wind speeds from 1.5 to 13.5 m/s and for mean grazing angles ranging from about 5º to 30º(Ogden and Erskine, 1994a, 1994b).

In this paper, sound scattering from the Persian Gulf’s sea surface is investigated. First, environmental conditions in this region are provided based on three different data bases. These conditions include information like wind speed and wave height, which are essential in this regard. Subsequently, based on various empirical relations and according to the mentioned data bases, sound scattering in the Persian Gulf region will be computed and analyzed. Provided results can have a broad range of implementation.

When a point source generates sound, or in another word disturbs its medium by producing an acoustic pressure, this sound or pressure disturbance is propagated in the medium. In a water medium located in the Ocean, there are different boundaries in its propagation range. As mentioned earlier, one of these boundaries is the sea surface. Therefore, when sound or pressure disturbance hits the sea surface, there are different parameters which determine how the emitted sound will be reflected or scattered. In acoustics, sound intensity I(w/m²)can be considered in order to determine the amount of carried energy per time and area units. This parameter can be considered in order to examine sound scattering from the sea surface. In order to accomplish this, the following relation can be applied(Medwin and Clay, 1998):

Here, I_s is scattered intensity at the receiver point, I_i the source intensity at a distance of 1m, r the range from the source to the scattering surface, A insonified area(m²), and S the surface backscattering strength(dB). These parameters are illustrated in Fig. 1. As pointed out earlier, different theoretical and experimental researches have been done in order to find an accurate surface scattering strength S for a realistic sea condition. This value determines the mean level of reverberation from the sea surface and calculating the scattered sound intensity is one of its applications.

θ1 is the incident angle and θ2 is the scattered sound angle with respect to the vertical axisFig. 1 Sound scattering from the sea surface

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CST experiments are some of the best known studies, which have been done by Ogden and Erskine and reported as CST-4 and CST-7(Ogden and Erskine, 1994a, 1994b). Their experiments resulted in very interesting conclusions that introduced at least three various regimes in sound scattering(as shown in Fig. 2):

Fig. 2 Frequency-wind speed(f -U)domain for sea-surface scattering strengths(Ogden and Erskine, 1994)

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1)In the first regime, results are generally consistent with scattering from a rough surface.

2)In the second regime, results are generally consistent with scattering from subsurface bubble cloud.

3)The third regime forms a transition zone between the other two regimes.

For relatively calm seas at high frequencies and for all wind speeds at lower frequencies, perturbation theory is found to give an accurate description of surface scattering. For rougher seas and higher frequencies, the Chapman-Harris empirical curves are adequate predictors of the levels of surface. Between these two regimes, there is a transition region where the scattering strengths are more difficult to predict, as they depend on the details of the surface and wind characteristics. This leads to the idea that there are two mechanisms that dominate the scattering of sound from the surface. In the perturbation theory regime, air-water interface scattering is the dominant mechanism and in the Chapman-Harris regime, another mechanism such as scattering from subsurface bubble clouds must dominate the scattering process. The transition region is then the part of the frequency and wind speed domain where the two effects are competing. Based on this conclusion, Ogden and Erskine(1994a) provided a diagram which is shown in Fig. 2.

However, classical approaches including Bass(1960), Marsh(1961), and Kuo(1988) mostly take into account the effects of sea surface roughness to find the scattering strength. In recent years, many studies have emphasized the importance of water plume. Duro et al.(2011) mentioned that since bubbles produce acoustic noise, they can affect sound characteristics such as phase speed. Also, subsurface bubble plume attenuates sound’s energy. Dol et al.(2013) stated that the subsurface bubble plume acts as an acoustic lens enhancing the rough surface scattering by the resulting upward refraction. Moreover, diffused screens and patchy clouds of air bubbles may form under the surface due to breaking waves(van Walree, 2013). In fact, due to breaking waves formed at the surface as a result of wind blow, the bubbles may start screening the sea surface and reduce the contribution of surface scattered to the received signal energy. This phenomenon is significantly essential in shallow water communication channels since the channel may completely become blocked(van Walree, 2013).

Therefore, in the recent decades, only those approaches are considered to be practical which can entail the influences of the subsurface bubble plume.

As mentioned earlier, perturbation theory(Brekhovskikh and Lysanov, 2003)was found to provide adequate description of the data at high frequencies for the calm seas, and at lower frequencies for all wind speeds where air-water interface scattering is the dominant mechanism. According to perturbation theory, the scattering strength(S_pert)is obtained as follows:

where S_pert is the surface scattering strength resulting by perturbation theory(dB), f is the frequency(Hz), θ is the grazing angle(degrees) and U is the wind speed(knots).

Chapman(1962) proposed an empirical relationship which can adequately describe surface back scattering for rougher seas at higher frequencies where scattering from the bubble clouds is presumed to dominate the scattering process(Ogden and Erskine, 1994a). The Chapman(1962) empirical relationship is defined as

In Chapman(1962) empirical relation like perturbation theory, U and θ are the wind speed(knot) and the grazing angle in degrees, respectively. The transition region where these two effects are competing, the scattering strengths depend on the details of the surface and wind characteristics.

Ogden and Erskine(1994b) proposed a relation based on the perturbation theory and Chapman-Harris’s scattering strengths which entails the effects of all three regimes for computing the total scattering strength at the sea surface. The proposed relation is as follows:

This formula is valid for grazing angles(θ)less than 40º for the wind speeds(U)less than 20(m/s)over the frequency range of 50 to 1000 Hz.

For practical applications, the algorithm uses a minimum wind speed of 2.5 m/s, since at lower wind speeds, swell is likely to dominate the scattering process. Fig. 2 shows the three regimes based on wind speed and frequency values. In the highest part of the f -U domain in Fig. 2(first region from the top in Fig. 2), only the Chapman-Harris formula should be used, that is α=1 in equation(5). In the lowest part of the f -U domain(third region from the top in Fig. 2), only the perturbation theory formula should be used, that is in equation(5). In fact, in the frequencies and wind speeds of this regime, surface roughness affects the quality of incident sound. Therefore, by considering α=0, the role of the subsurface bubbles is ignored, since it does not have any significant effect on the scattering strength value(Etter, 2003). In the third regime(second region from the top in Fig. 2), which is called the transition region, α should be determined based on equation(6). In this way, the combination of both perturbation theory and Chapman-Harris’s scattering strengths determines the total value of the scattering strength. In this condition, U is the wind speed of the intended region and U_pert and U_CH are wind speeds of perturbation theory and Chapman-Harris that are determined by the frequency value, respectively.

For convenience, Ogden and Erskine(1994b) put together perturbation theory and Chapman-Harris boundaries into analytical forms as follows:

The upper boundary was approximated by the cubic equation:

Based on equations(7) and (8), it is possible to determine U_pert and U_CH in transition region. Actually, frequency is used to determine these values, which implies that the frequency has a significant role in the transition region. In another word, frequency not only determines which regime is being dealt with but is also involved in computation of the value of scattering strength.

In the following section, environmental conditions in the Persian Gulf region based on different data bases are discussed. This conditions will be used later in order to study sound scattering in this region according to provided empirical expressions.

The Persian Gulf is located in the Middle East in southern part of Iran, as shown in Fig. 3. This Gulf is connected to the Indian Ocean through the Oman Sea. This inl and sea of some 251 000 km² is connected to the Gulf of Oman in the east by the Strait of Hormuz and its western end is marked by the major river delta of Arv and which carries the waters of Euphrates and Tigris rivers. Its length is 989 km with Iran covering most of the northern coast and Saudi Arabia of the southern coast. Persian Gulf is about 56 km wide at its narrowest in the Strait of Hormuz. Waters are overall very shallow in this region with a maximum depth of 90 m and an average depth of 10 m(Zhang, 2011). The Persian Gulf and its coastal areas are the world’s largest sources of crude oil and its related industries are dominating in this region. Large gas sources exist with Qatar and Iran sharing a giant field across the territorial median line.

Fig. 3 Persian Gulf geographical location(Zhang, 2011)

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The Persian Gulf has relatively warm weather and seasonal north-west winds are the most powerful winds, which mostly blow in summer and winter. From November to March, seasonal winter winds blow from west to east. This phenomenon creates cold weather fronts, which causes seasonal north-west winter winds to blow in December, January, and February. Seasonal summer winds which usually blow from the beginning of June to middle of July are weaker than seasonal winter winds that occur due to low pressure thermal condition in the Indian Ocean and Oman Sea.

Annual and seasonal wind rose plots reported by the Arzanah station in 5 years period during 2003 to 2007 are shown in Figs. 4 and 5, respectively. Also, Table 1 presents the hourly wind speeds and the annual and seasonal gusty winds information reported by the Arzanah station.

Fig. 4 Annual wind rose plot reported by Arzanah station during 2003 to 2007(Golshani, 2010)

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Fig. 5 Seasonal wind rose plots reported by Arzanah station during 2003 to 2007(Golshani, 2010)

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There are other data bases or sources besides the Arzanah station. Numerical models such as ERA40 and PERGOS provide data which can be accessed freely on their websites(ECMWF website, 2009; NOAA website, 2009; Ocean Weather website, 2009; PODAAC QuikSCAT website, 2009). Different features of these data bases are provided in Table 2. Table 3 provides the wind speed information from each data base. Wind rose plots resulting from the numerical models ERA40 and PERGOS are shown in Fig. 6.

Fig. 6 Wind rose plots according to:(a)NCEP/NCAR, (b)ERA40, (c)PERGOS, (d)QUIKSCAT(Golshani, 2010)

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As mentioned in the previous section, wind speed is an essential input of the provided empirical relations in order to obtain surface scattering strength. Since in the current section, all the necessary data related to wind speed is presented based on available data bases, it is possible to study sound scattering in the Persian Gulf region. Therefore, in the following section, sound scattering from Persian Gulf region will be discussed and applied in order to calculate the proper surface scattering intensity.

In this section, results of surface scattering strength calculated by the presented approaches in Section 2 are verified by the CST-7 experimental tests which have been conducted in the Gulf of Alaska by Ogden and Erskine(Ogden and Erskine, 1994b). First, the accuracy of the Ogden and Erskine’s(OE)empirical relation(equation(5))is verified by the CST-7 results. Subsequently, in section 5, OE’s empirical relation will be applied in order to examine scattering strength in the Persian Gulf region.

In order to implement the validation process, three different runs from CST-7 which consist of twenty runs, are chosen. The environmental conditions of the selected runs are provided in Table 4. Since these runs are selected to cover all three regimes discussed in section 2, it would be possible to examine accuracy of the OE’s empirical relation in various conditions.

Fig. 7 shows the scattering strength results based on perturbation theory, Chapman-Harris(CH), and Ogden-Erskine(OE)approaches as well as CST-7(16B)at 158 Hz frequency and wind speed 17.5 m/s. According to Fig. 2, at these conditions, the second regime is dominant. Therefore, it is anticipated that CH’s approach gives more accurate results. As evident in Fig. 7, results of both CST-7(16B) and OE’s empirical relation are closer to CH’s results. Fig. 8 depicts the results of scattering strength at frequency of 962 Hz and wind speed 17.5 m/s. Like Fig. 8, at this frequency and wind speed, the second regime is dominant. Similar as in the case of Fig. 7, results of CH approach are consistent with CST-7 and OE’s results.

Fig. 7 Scattering strength(dB)according to CST-7(16B) setup at wind speed 17.5 m/s and frequency 158 Hz

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Fig. 8 Scattering strength(dB)according to CST-7(16B) setup at wind speed 17.5 m/s and frequency 962 Hz

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In Fig. 9, the conditions of CST-7(23C)test are considered at 154 Hz frequency and wind speed of 8 m/s. Based on Fig. 2, first regime is dominant. In this case, α is α=0.09 which indicates that in equation(5), the scattering strength from perturbation theory S_pert, has major role in total scattering strengthS_total. Therefore, the total scattering strength S_total is more consistent with the values of S_pert. However, in Fig. 10 which depicts the scattering strength results at a higher frequency of 934 Hz, the third regime is dominant, as shown in Fig. 2. As stated, since both surface roughness and subsurface bubble plume are involved in this regime, the total scattering strength is determined by combination of both S_pert and S_CH. Consequently, the CST-7(23C) and OE’s curves are between the other two curves of scattering strengths, as shown in Fig. 10.

Fig. 9 Scattering strength(dB)according to CST-7(23C) setup at wind speed 8 m/s and frequency 154 Hz

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Fig. 10 Scattering strength(dB)according to CST-7(23C) setup at wind speed 8 m/s and frequency 934 Hz

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Figs. 11 and 12 show the scattering strength results based on CST-7(25D)test conditions. In Fig. 11, results of scattering strength are depicted at frequency of 154 Hz. Since wind speed is 3 m/s in this case, based on Fig. 2, the first regime is dominant. Consequently, as depicted in Fig. 11, results of both total scattering strength and CST-7(25D)test are more consistent with perturbation theory which plays the major role in the first regime where surface roughness mechanism determines the quality of the scattering strengths. Fig. 12 shows the results of scattering strength at the same wind speed as in Fig. 11, but the frequency is increased to 942 Hz. However, in this case, the first regime’s dominance does not change and perturbation theory offers more accurate results compared to the results of CH.

Fig. 11 Scattering strength(dB)according to CST-7(25D) setup at wind speed 3 m/s and frequency 154 Hz

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Fig. 12 Scattering strength(dB)according to CST-7(25D) setup at wind speed 3 m/s and frequency 942 Hz

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Based on the provided results in Figs. 7 through 12, it can be concluded that all the mentioned approaches generally have the same trend. In fact, as the grazing angle, frequency, and wind speed increase, the resulting scattering strengths increase. However, it is the surface roughness and subsurface bubble mechanisms which determine the quantitative values of the total scattering strength at various wind speeds, frequencies, and grazing angles. As observed in Figs. 7, 8 and 10, the perturbation method has a noticeable deviation from the experimental data, which is due to the fact that perturbation method does not take into account the subsurface bubbles.

In the previous section, Ogden and Erskine’s empirical relation(Ogden and Erskine, 1994b)based on Perturbation theory and Chapman-Harris’s approach in different scattering regimes was applied to obtain the total scattering strength S_total. Also, the findings were verified using the results of three various runs of the CST-7 experimental tests. In this section, based on the provided environmental information of the Persian Gulf in section 3, scattering strength and scattered intensity in this region are discussed. In fact, the results of scattering strength are obtained by Perturbation theory, Chapman-Harris and Ogden-Erskine approaches and finally the resulting total scattering strengths S. It is utilized as the inputs of equation(1)in order to calculate the scattered intensity I_S from the Persian Gulf’s surface. Parameter I_S is one of the essential variables in underwater communication channels, sonar performance, seismic investigation, and oceanography.

Figs. 13-15 represent the results of scattering strength in the Persian Gulf, based on the provided information by the three mentioned data bases in the previous section. In these figures, in spectral region of 200 to 1000 Hz, five different frequencies with equal steps of 200 Hz are considered and total scattering strength results vs. grazing angle at the reported wind speeds by the three data bases are calculated. Furthermore, since scattering strengths of the perturbation theory do not vary significantly as the frequency increases, the provided curves of perturbation theory in Figs. 13 through 15 represent all the frequencies in spectral range of 200 to 1000 Hz. However, results of the Chapman-Harris are highly dependent on the frequency. Therefore, its results are depicted in Figs. 13 through 15 at the maximum and minimum of the considered frequency ranges.

In Fig. 13, results of scattering strength are based on the maximum and mean values of the reported wind speed by Arzanah station data base. In Fig. 13(a), at wind speed of 17.5 m/s and all the considered frequencies, the second regime is dominant. Therefore, it is reasonable that scattering strength results are more consistent with the total results of CH rather than the perturbation theory. On the other h and, in Fig. 13(b)which represents the results according to the mean wind speed of 4.68 m/s reported by Arzanah station, first regime is dominant. Consequently, the surface roughness is the dominant mechanism. Since perturbation theory is based on this mechanism, its results are in a better agreement with OE’s results of the total scattering strength than the CH’s results.

Fig. 13 Scattering strength results based onArzanah Station data base

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Fig. 14 provides the scattering strength results based on ERA40 data base. According to this data base, maximum and minimum wind speeds are 15.03 m/s and 4.52 m/s, respectively. Based on Fig. 2, it can be concluded that at frequency range 200 Hz to 1000 Hz and at wind speed of 15.03, the second regime is dominant. Consequently, as evidenced in Fig. 14(a), results of CH are found to be the accurate results. Fig 14(b)depicts the results of scattering strength at the mean reported wind speed by ERA40, where the second regime is dominant. Therefore, the surface roughness is the dominant mechanism. Fig. 15 represents the results of scattering strength at the reported wind speeds by numerical PERGOS data base. Based on the considered wind speed in Figs. 15(a) and 15(b) and according to Fig. 2, it can be concluded that the second and the first regimes are dominant at wind speeds of 15.99 m/s and 4.35 m/s, respectively.

Fig. 14 Scattering strengthresults based on ERA40 data base

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Fig. 15 Scattering strength results based on PERGOS data base

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As pointed out earlier, one of the scattering strength applications is the calculation of the scattered intensity from the sea surface. This basically means that scattered intensity can be obtained through inserting total scattering strength S in equation(1)by knowing the sound pulse with initial intensity I_i, grazing angle θ, insonified area A and frequency f. Therefore, based on the total scattering strength results which are presented in Figs. 13 to 15, it is possible to determine the scattered intensity I_S in the Persian Gulf region. As discussed in section four, the most accurate empirical relation, which takes both surface roughness and subsurface bubble plume mechanisms into account, to calculate the total scattering strength thus far is the one provided by Ogden and Erskine(1994b).

Figs. 16 to 18 illustrate the scattered intensity vs. grazing angle in spectral region 200 Hz to 1000 Hz, based on the OE’s total scattering strength results shown in Figs. 13-15. As pointed out earlier, In order to compute the scattered intensity, it is imperative to determine the quantitative data of source depth(r) and the insonified area(A). The Persian Gulf is considered as a shallow water region and as mentioned before, the maximum and mean depths in this region are 90 m and 10 m, respectively. For the source location r, an arbitrary value equal to the mean depth 10 m in the Persian Gulf is considered for the provided data in Figs. 16 to 18. Also, through a simple geometric calculation and by knowing the grazing angle θ, and the source location r, it is conceivable to calculate the insonified area A.

Fig. 16 Scattered intensity results based on Arzanah data base

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Fig. 17 Scattered intensity results based on ERA40 data base

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Fig. 18 Scattered intensity results based on PERGOS data base

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Fig. 16 depicts the results of scattered intensity I_S based on the total scattering strengths of Fig. 13, which are according to Arzanah station data base. In fact, both the maximum and the mean wind speeds of the Arzanah station are considered in order to calculate the scattered intensity. As evident in Fig. 16, at both of these wind speeds, the scattered intensity generally increases as the grazing angle and the frequency increase. Also, it is quite interesting that at maximum wind speed of 17.5 m/s, which implies higher sea state, the values of the scattered intensity are higher than the ones based on the mean wind speed 4.68 m/s. This may be attributed to the motion of the sea surface modulating amplitude fluctuations of a speedy signal, with upper and lower sideb and s having the same spectrum as the motion of the sea surface(Etter, 2003). Consequently, although at rough sea surfaces, the quantity of the scattered intensity is higher, its quality declines. This phenomenon which may occur due to the subsurface bubble plume is significantly crucial in communication channels in which the scattered intensity from the rough sea surface has too much noise which negatively affects the performance of the channel(van Walree, 2013).

Fig. 17 provides the scattered intensity based on the ERA40 data base. The maximum and mean wind speeds of the ERA40 data base are less than those reported by the Arzanah station. This causes general reduction in the scattered intensity which occurs as the result of total scattered strength reduction. Fig. 18 represents the scattered intensity based on the total scattered strength resulting from the reported wind speed by the PERGOS data base. Since the maximum and mean wind speeds of this data base are less than those of Arzanah station data base and higher than those of the ERA40 data base, the resulting scattered intensities based on PERGOS data base are between the results of the scattered intensity of the other two data bases.

The aim of the current study is to investigate the sound scattering in the Persian Gulf region based on empirical relations. Chapman-Harris, Perturbation theory and Ogden-Erskine’s scattering relations are discussed. Ogden and Erskine(1994) through CST-7 experiments concluded that there are three different regimes in sound scattering from the sea surface which function based on the two mechanisms of surface roughness and subsurface bubble clouds effects. After studying the scattering mechanisms and regimes, Ogden-Erskine’s scattering relation based on perturbation theory and Chapman-Harris’s scattering terms is verified by three various runs of CST-7 experimental tests that have different environmental conditions. Compared to real data of CST-7 runs, the Ogden-Erskine’s scattering strength relation gives highly accurate results at different regimes. Based on these studies, it is concluded that as wind speed, frequency, and grazing angle increase, the scattering strength increases. Therefore, Ogden-Erskine’s scattering relation is an appropriate approach to study the scattering strength in the Persian Gulf’s environmental conditions in which all three scattering regimes exist. Annual wind speed rose plots in this region are provided based on three data bases: Arzanah station information, ERA40 and PERGOS numerical atmospheric models. The analyzed mean and maximum wind speeds from these data bases are considered as the input of Chapman-Harris, perturbation theory and Ogden-Erskine scattering strength relations. Accordingly, scattering strengths at these wind speeds, various grazing angles and frequencies are computed and their plots are presented. Furthermore, the obtained values of total scattering strength are taken into account in order to calculate the scattered intensity I_S in the Persian Gulf. The results indicated that as wind speed, frequency and grazing angle increase, the scattered intensity generally increases.