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Numerical Investigation of Wind Waves in the Persian Gulf: Bathymetry Effects

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  • 1 Zachry Department of Civil Engineering, Texas A&M University, College Station, Texas
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Abstract

The effects of bathymetry on the process of wind-wave generation in the Persian Gulf have been investigated using a long-term hindcasting analysis. A 5-yr (2004–08) hindcasting procedure is first performed (denoted as origin) by using the Simulating Waves Nearshore (SWAN) model and COAMPS wind field data. Two alternative scenarios, in which wave breaking (noBrek) and depth-induced refraction (noRefc) are deactivated, are also generated. By comparing the results from alternative cases with those from the ordinary cases, a 5-yr total energy deviation (TED) is calculated and presented as seasonal contour maps depicting the sensitivity to bathymetry. The results show only ±2% TED found in noBrek, but up to ±20% TED found in noRefc, an order of magnitude larger than depth-induced breaking. Similarly, the seasonal effects of refraction on the nearshore wave-propagating directions can be investigated by comparison between origin and noRefc. The seasonal histograms of mean wave angle are plotted and discussed for three selected nearshore sites around Qatar, located at the western, northern, and eastern sides of the peninsula. The largest relative occurrence percentage and the largest peak shift ranging in 10°–20° can be found at the northern side, while the eastern side results in a weaker and more random distribution in the winter (the strong shamal season) due to the leeside location. The effect of fetch-limited wind-wave generation is also present at the eastern site, as remotely generated waves propagating eastward over a long fetch toward this site offset southward-propagating waves generated by dominant winds from the north over a limited fetch.

Corresponding author address: Ying-Po Liao, Zachry Department of Civil Engineering, Texas A&M University, 3136 TAMU, College Station, TX 77843-3136. E-mail: lrobin@neo.tamu.edu

Abstract

The effects of bathymetry on the process of wind-wave generation in the Persian Gulf have been investigated using a long-term hindcasting analysis. A 5-yr (2004–08) hindcasting procedure is first performed (denoted as origin) by using the Simulating Waves Nearshore (SWAN) model and COAMPS wind field data. Two alternative scenarios, in which wave breaking (noBrek) and depth-induced refraction (noRefc) are deactivated, are also generated. By comparing the results from alternative cases with those from the ordinary cases, a 5-yr total energy deviation (TED) is calculated and presented as seasonal contour maps depicting the sensitivity to bathymetry. The results show only ±2% TED found in noBrek, but up to ±20% TED found in noRefc, an order of magnitude larger than depth-induced breaking. Similarly, the seasonal effects of refraction on the nearshore wave-propagating directions can be investigated by comparison between origin and noRefc. The seasonal histograms of mean wave angle are plotted and discussed for three selected nearshore sites around Qatar, located at the western, northern, and eastern sides of the peninsula. The largest relative occurrence percentage and the largest peak shift ranging in 10°–20° can be found at the northern side, while the eastern side results in a weaker and more random distribution in the winter (the strong shamal season) due to the leeside location. The effect of fetch-limited wind-wave generation is also present at the eastern site, as remotely generated waves propagating eastward over a long fetch toward this site offset southward-propagating waves generated by dominant winds from the north over a limited fetch.

Corresponding author address: Ying-Po Liao, Zachry Department of Civil Engineering, Texas A&M University, 3136 TAMU, College Station, TX 77843-3136. E-mail: lrobin@neo.tamu.edu

1. Introduction

The Persian Gulf is geographically located between the Arabian Peninsula and Iran, surrounded by Iran, Iraq, Kuwait, Saudi Arabia, Qatar, and the United Arab Emirates. It is a long semienclosed basin with a narrow opening (Strait of Hormuz) at the south passage, connecting to the Gulf of Oman and Indian Ocean. Because of the large oil and gas reserves present, the Persian Gulf is an important natural and economic resource. The wind-wave conditions are therefore of interest. The conditions in this area are dominated by a mesoscale meteorological phenomenon known as the shamal, a strong northwesterly wind occurring primarily in winter, with some occurrences in summer. El-Sabh and Murty (1989) and Thoppil and Hogan (2010) show that the summer and winter shamals have different characteristics, as they have different average velocities. The winter shamal is stronger with 5 m s–1 average velocity, while the summer shamal is weaker with 3 m s–1 average velocity (Thoppil and Hogan 2010). However, there is no consistent definition of duration for winter and summer shamal seasons. The time span of the winter shamal is loosely defined but generally accepted as starting in November. In contrast, the summer shamal is generally defined to be between June and September. Preliminary work by the authors suggest that the winter and summer seasons can be defined as 1) winter: November–March; 2) spring: April and May; 3) summer: June and July; and 4) fall: August–October. The periods conform to the definitions given by El-Sabh and Murty (1989).

Given the deficiency of long-term basinwide wave measurements and meteorological observations, a combination of numerical models with observations can be a useful substitute for understanding the wind-wave processes in this area. El-Sabh and Murty (1989) investigate storm surge using linearized two-dimensional shallow-water equations forced by wind stress. This approach, however, is not able to solve wave-scale problems. The Wave Model (WAM; The WAMDI Group 1988) has been widely used to simulate random wave processes. Phase-averaged random wave models like WAM solve the wave energy (or action) transport equation, forced by energy sources (from wind) or sinks (from dissipation). Studies of extreme waves by numerical hindcast using WAM in the Persian Gulf have been conducted by Neelamani et al. (2007a,b) for the entire basin and the Kuwaiti regional area, respectively. In a contrasting approach, Parvaresh et al. (2005) performed a statistical study on the wave parameters through the analysis of wind and wave measurements using time series regression models. Rakha et al. (2007) performed a numerical hydrodynamic study by combining wave model WAM and hydrodynamic model RMA-10 (Resource Modeling Associates). In addition to tidal currents and water level, wave attributes such as significant wave height and wave periods were also studied.

In contrast to WAM, the Simulating Waves Nearshore (SWAN) model (Booij et al. 1999; Ris et al. 1999) includes many aspects of shallow-water physics, including refraction, depth-limited breaking, and shallow-water nonlinearity, making it ideal for the coastal areas of the Persian Gulf. The model has been used in several studies in the Persian Gulf. Moeini et al. (2010) have used SWAN to perform wave hindcasts for the Persian Gulf. Two data sources of surface wind were used as forcing. By comparing with measurements of wave data, the quality of wind data sources and model calibration was assessed. Through statistical analysis of the numerical results, extreme waves with various return periods were also studied. Kamranzad et al. (2013) performed a 25-yr long-term hindcasting exercise using SWAN and ECMWF winds to extract the wave characteristics spatially and temporally, where output wave parameters are validated by buoy data at selected sites along the northern coast of the Persian Gulf. They used the results to quantify the available wave power for possible energy extraction.

One aspect of wave prediction in this region that has not been studied is the effect of bathymetric variation on the results. Given the small size of this nearly enclosed basin, it is not immediately clear whether sufficiently long swell would be generated such that the resolution and quality of the bathymetry would be a concern. There are few bathymetric surveys of coastal regions in the area. As bathymetric information is sparse, such an effort can highlight the importance of accurate surveys for the area. Furthermore, the flexibility of the model allows for the deactivation of bathymetrically induced propagation effects, so that the influence of bathymetry can be ascertained. For a semienclosed, straight, long, and flat basin such as the Persian Gulf, it is worth investigating how the bathymetric effects determine the result of wind-wave conditions. In addition, deactivation of terms considered negligible in certain parts of the domain can achieve computational savings, so investigation into the possibility is useful. Finally, determination of the effect of bathymetry relative to the effect of wind on wave propagation in the nearshore area can be useful in determining the necessary resolution and quality of wind information for modeling.

The effect of bathymetric variation of wave and wave-driven processes has been widely studied. Despite the variation in focus, many studies have used SWAN. Gorrell et al. (2011) discussed the complex bathymetric effects at Scripps Canyon by comparing directional wave buoy observations and numerical predictions. Similarly, focusing on the regional wave response caused by a complex bathymetry in La Jolla, California, Kaihatu et al. (2002) used SWAN to perform a sensitivity analysis in which the boundary-driving spectra for the offshore conditions are discretized using different directional resolutions, and the nearshore wave processes are studied correspondingly. Rogers et al. (2007) apply a multilevel approach in which three different levels of grid nesting are used to improve the predictive capability of the SWAN model for nonstationary wave propagation through the Southern California Bight. The errors due to uncertainty in bathymetry are also discussed via the comparison to buoy data. The sensitivity of nearshore wave processes due to different scales of bathymetric variability has also been studied. Plant et al. (2009) studied the alongshore and cross-shore wave and hydrodynamic sensitivity by applying bathymetric filtering in different degrees of smoothing, while Manian et al. (2012) derived optimization schemes using genetic algorithms to reduce the bathymetric sampling required in nearshore wave and hydrodynamic modeling. Both studies were conducted using Delft3D (Lesser et al. 2004) in which SWAN was the wave driver. Moreover, the resolution of bathymetry and the underlying uncertainty are the determining factors. Both van Dongeren et al. (2008) and Orzech et al. (2014) performed similar studies. In particular, Orzech et al. (2014) employed SWAN for the proposed assimilation algorithms, and furthermore generated sensitivity maps to show the dependence of bathymetric resolution of special statistics.

The purpose of this study is to understand the effects of bathymetrically controlled processes, such as depth-induced breaking and refraction, on the seasonal characteristics of the wave climate in the Persian Gulf, with particular focus on the coastal areas of Qatar. A 5-yr wave hindcast from 2004 to 2008 is performed using SWAN, forced by winds from the COAMPS model (Hodur 1997). While there is a notable lack of observations in the area for comparison, we perform comparisons with models using refraction and depth-limited breaking mechanisms activated to ascertain the importance of bathymetric information.

In section 2, the study area and data sources used in SWAN are discussed. In this section, the COAMPS model (Hodur 1997) is introduced. In section 3a, the SWAN model is described. The corresponding model configurations are also explained in section 3b. In addition to the study of seasonal wave climates through standard hindcasting (refraction and breaking activated), alternative scenarios are set up and performed to investigate the sensitivity resulting from bathymetric variation. In addition, we also investigate the effect of the resolution of the input bathymetry by subsampling the bathymetric field and interpolating the result to the resolution of the computational grid. This will offer some evaluation of the importance of the bathymetric resolution on refraction processes in the gulf. In section 4 we discuss the numerical results in two ways: 1) seasonal bathymetry effects at the basin scale due to depth-induced breaking and refraction, and 2) the local effects due to refraction around Qatar. Concluding remarks are made in section 5.

2. Study area and data preparation

a. Study area and bathymetric data

As mentioned above, the Persian Gulf is a long, flat, and shallow semienclosed basin, located between 24°–30°N and 48°–57°E, whose width varies from 56 to 338 km, the central axis reaches 990 km long, the total area covers about 226 000 km2, and the average water depth is 35 m. The Strait of Hormuz, located in the south of the basin with a narrow opening of 56 km, is the only passage connecting the Persian Gulf to the Gulf of Oman and the Arabian Sea. Figure 1 shows the area.

Fig. 1.
Fig. 1.

The bathymetry and computational domain of the study area.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

The ETOPO1 database (Amante and Eakins 2009) is used for bathymetric information, which has a resolution of one arc-minute in both latitude and longitude and a vertical resolution of approximately 10 m. There are no additional datasets for bathymetry to add additional detail to the coastal database. However, since we are applying this same database to both standard and alternative hindcasting scenarios, this lack of detail does not affect our conclusions.

b. Time frame and hindcasting winds

The quality and characteristics of the wind field input has a major influence on the ensuing wave hindcast. In this study we employ wind field data generated from the numerical model COAMPS (Hodur 1997). COAMPS is an ocean–atmosphere coupled mesoscale weather model developed by the Naval Research Laboratory. The model integrates the physics of mesoscale atmospheric dynamics with a data assimilation scheme to improve the accuracy of the solution.

The 5-yr reanalysis data from 2004 to 2008 generated by COAMPS have been assimilated with the observations and is used as wind input in SWAN. The temporal resolution and spatial resolution of the wind input are 12 h and 0.2° × 0.2°, respectively. The width of the Persian Gulf is about 2°, or 10 × 10 grids per arc-degree square. For model input, COAMPS data are linearly interpolated to the established computational spatial and temporal resolutions. Compared to previous work in this area (Neelamani et al. 2007a,b; Moeini et al. 2010; Kamranzad et al. 2013), which use European Centre for Medium-Range Weather Forecasts (ECMWF) winds as input, COAMPS offers somewhat higher spatial resolution, which is important in representing orographic effects such as the mountains of neighboring Iran.

3. Model description

a. SWAN model

The SWAN model (Booij et al. 1999; Ris et al. 1999) is a third-generation wind-wave model developed specifically for coastal regions. The wave evolution is solved in terms of action density spectrum transport in different dimensions. SWAN is an advance over WAM (Komen et al. 1996) due to its higher-order numerics (Rogers et al. 2002) and the inclusion of refraction effects from currents and bathymetry. Action density spectrum is given by , where σ is the intrinsic frequency. The governing equation for the SWAN model is written as
e1
The first term on the left-hand side is the local rate of change of action density in time, the second and the third terms describe the spatial variations of action density with propagation velocities and along the λ and φ dimensions, respectively. The fourth term represents the shifting of relative radian frequency arisen from depth and current variations, with propagation velocity along the σ dimension. The fifth term accounts for the depth-induced and current-induced refraction in which action density transports along the θ dimension with propagation velocity .

The right-hand side is the source term in which is the energy density added or dissipated. This term represents the effects of 1) generation—for example, linear and exponential wind growth; 2) dissipation—for example, whitecapping, bottom friction, and depth-induced breaking; and 3) nonlinear wave-wave interactions—for example, triad and quadruplet wave-wave interactions.

b. Model configuration

SWAN cycle III, version 40.81, is employed in this study (SWAN Team 2012). The simulation of two-dimensional nonstationary waves with spherical coordinates is performed in the third-generation mode. The time step of computation is selected as 20 min throughout the 5-yr simulation from 1 January 2004 to 31 December 2008; finer temporal resolutions revealed no appreciable differences. Regular discretization is used for both the spatial and spectral domains. The spatial domain is bounded between 24°02′–29°17′N and 47°01′–57°42′E, and the discretized domain into 641 × 315 cells with 1′ × 1′ spatial resolution. For the spectral domain, the spectral direction is equally divided into 36 subdivisions around a circle in which ; the frequency dimension is bounded between 0.06 and 1 Hz, and for the grid resolution 36 discrete frequencies are logarithmically distributed along σ space. The results are output every 3 h.

For the wind input in the source term, SWAN describes the mechanism as a combination of linear and exponential parts, formulated as . In this study we both use active linear and exponential growth. The expression for linear growth term A is formulated by Cavaleri and Rizzoli (1981), and the expression of exponential growth term B is that of Komen et al. (1984). In addition, action density dissipation due to depth-induced wave breaking, bottom friction, and whitecapping are also considered in the source term.

Furthermore, in addition to the standard hindcasting mode (denoted as origin below), two alternative scenarios are carried out as well; these help investigate the importance of bathymetric variation. One is to switch off the refraction (denoted as noRefc below) and the other is to switch off depth-induced wave breaking (denoted as noBrek below). The rest of configurations are identical to the origin case.

In terms of computational load, we have 131 544 time steps calculated for more than 225 × 103 grid points, for each of the three scenarios. Considering such massive computations, a message passing interface (MPI) parallelization version of SWAN with eight processors is employed to perform for each scenario.

4. Results and discussion

The shamal is the most persistent meteorological event for the region. It thus seems logical to use it as a means of categorizing the wave climate (and the resulting effects of bathymetry) over the course of the year. As stated previously, we define a “summer shamal” season as June–July, and a “winter shamal” season as November–March. Other months are identified as “nonshamal” months.

a. Basin-scale investigation

The first step is to establish a metric for evaluating the difference between the standard and alternative scenarios. The average energy density per unit horizontal area is defined as
e2
Therefore, given a grid point at , the 5-yr total energy deviation (TED) for either case noBrek or case noRefc can be approximated by
e3
where n loops over all values in the time series. In this equation, indicates the values given by either case noBrek or case noRefc, while variables without a bar denote the values from reference case origin.

Figures 2 and 3 show the maps of percentage of 5-yr TED for case noBrek and case noRefc, respectively. Figures 2a and 3a show the total 5-yr results, while Figs. 2b–d and 3b–d show the 5-yr seasonal results for the nonshamal season (months 4, 5, 8–10), the summer shamal season (months 6 and 7), and the winter shamal season (months 11, 12, 1–3), respectively. In addition, in order for better comparison and explanation, we also performed the 5-yr seasonal averaged analysis for winds and wave heights. Figure 4 shows the 5-yr average wind speed and average wind direction, and Fig. 5 shows the 5-yr average significant wave height, both divided into the defined seasonal months.

Fig. 2.
Fig. 2.

The 5-yr TED (%) for case noBrek.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

Fig. 3.
Fig. 3.

The 5-yr TED (%) for case noRefc.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

Fig. 4.
Fig. 4.

The 5-yr average wind speed (m s−1) and wind direction.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

Fig. 5.
Fig. 5.

The 5-yr average significant wave height (m).

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

As wave breaking dissipates wave energy, turning off wave breaking would generally result in an overprediction of wave energy (positive TED) in regions where the water depth would be conducive to breaking. Figure 2 shows that most of the area is of positive TED percentage for the case noBrek. Moreover, the regions of higher TED due to wave breaking are mainly distributed 1) behind islands, 2) at the nearshore coasts, and 3) near the pass of the Strait of Hormuz. Compared to the summer, in the winter there are more areas in the domain in which TED due to wave breaking surpasses 2%, particularly around the islands east of Qatar, as well as in the southern area near Strait of Hormuz between 54.5° and 56.5°E. The most apparent differences are seen in the nonshamal seasons, as shown in Fig. 2b. At the Strait of Hormuz, a large amount of wave breaking takes place at the pass between Iran and Oman.

A possible explanation for the higher degree of positive (blue) TED in the strait during the nonshamal season is largely due to the differences in the wind forcing between the seasons. For shamal seasons, the waves are propagating mainly from the north through the southern part of the Persian Gulf, encountering the small islands and breaking, then propagating through the strait. However, for nonshamal season the entire Persian Gulf experiences smaller waves, as shown in Figs. 4b and 5b; this can lead to a higher TED in the strait. In additional, winds and waves have a much broader directional range during nonshamal seasons because they are lacking dominant meteorological features; as a result, they may not have been propagating over the small islands offshore of Iran (54°–55°E) and are likely not uniformly affected by the same bathymetric features.

The large area of negative TED (in red) in the Gulf of Oman is also possibly due to the lack of a systematic meteorological feature during nonshamal seasons. Furthermore, the negative TED indicates that the noBrek case has lower energy than the origin case, which may be due to the effects of whitecapping in the model reducing higher unbroken waves.

For the shamal cases, there also appears to be higher TED values along the Saudi Arabian coast (27°–29°N, 49°–50°E) than in the nonshamal cases, indicative of higher wave energy (and more coastal wave breaking). It can be seen that several very small shallow island-like areas, as well as a broad shelf, are inducing breaking of higher waves caused by the shamal, leading to notable TED values. However, the TED values for noBrek do not exceed ±2%, indicating that the effect of bathymetry via depth-induced breaking is small.

Figure 3 shows seasonal contour maps of TED due to refraction. Compared to the range of TED values due to wave breaking (±2%), the range of TED values due to refraction is much larger (±20%). Areas with positive TED (blue) indicate regions from which refraction would move energy, while negative TED (red) indicate regions into which refraction would channel energy. For example, in the northeastern region of Qatar, TED is <−20% in the wintertime. It implies that in the wintertime over 20% of wave energy brought to this area is due to wave refractions. In contrast to the case noBrek that mainly results in positive TED, the TED patterns in the case noRefc show TED values that are both plus and minus. Nonzero TED can be found in most of the shallow areas; the ribbonlike patterns indicating a high degree of spatial variability of the refraction effect in the nearshore. The high degree of TED variability appearing along the southwestern coast of the Persian Gulf is largely due to the broad shelf in this region. The Persian Gulf is deepest near the Iranian coast (Fig. 8) and thus does not show substantial TED. The spatial TED patterns for the case noRefc do not appear to change with seasons. Seasonal differences can generally be seen only in magnitudes, with the nonshamal seasons seeing smaller TED than the two shamal seasons.

To evaluate the bathymetry data sensitivity of ETOPO1 to the analysis results, we also designed a subsampled case for comparison as mentioned previously. Here, we reduce the resolution of the ETOPO1 bathymetry by a factor of 2 and gauge the effect on the wave heights. We note that the subsampled bathymetry was interpolated to the same computational grid resolution as the origin case, so the differences are not due to reduced numerical accuracy. Figure 6 shows the absolute difference percentage of bathymetry between the origin case and the subsampled, interpolated case. It is apparent that the effects of reducing the bathymetric resolution are primarily in the nearshore areas. Figure 7 shows the 5-yr TED between the subsampled case and the origin case. The general trend shows that, irrespective of the season, lower TED values are consistently confined to the deeper regions of the Persian Gulf. In contrast, the high values of TED are located on the shelf near the southwestern coast of the Persian Gulf. There is also a high degree of spatial variation in this TED evaluation relative to that in comparison to the noRefc case. The wave height field for noRefc would have little spatial variation, so differences between the noRefc mean energy field and that of origin would have a similar lack of variability. In contrast, both refraction cases for both origin and the subsampled bathymetry would have variability in line with that of bathymetry, thus evaluation of their differences in energy would display similar spatial variability.

Fig. 6.
Fig. 6.

The absolute difference (%) of subsampled bathymetry. Errors larger than 10% are shown as solid blue.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

Fig. 7.
Fig. 7.

The 5-yr TED (%) for subsampled case.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

b. Local investigation around Qatar

To take a closer look at the influence of any bathymetrically induced effects (refraction in particular) on local wave angles, we selected three nearshore locations at which to measure wave statistics. As shown in Fig. 8, they are Hawar Island (25.7660°N, 50.8349°E; water depth of 13.85 m), Ras Laffan (25.9340°N, 51.5593°E; water depth of 3.09 m), and Doha Port (25.3300°N, 51.6100°E; water depth of 2.02 m), located on the western side, northern side, and eastern coastline of Qatar, respectively. We use mean wave angle as a means of gauging the effect of refraction on nearshore wave prediction. The results are shown using the SWAN model convention: 0° is due east and the directions indicate those in which the waves are propagating toward. The histograms of and their corresponding winds for the three selected sites are plotted in Figs. 911. The magnitude in the histograms is defined by the relative occurrence percentage per degree . Given a bin i, is defined by , where is the number of occurrence for bin i, N is the total number of occurrence, and is the width of bin i. We first compare the origin and noRefc cases at all sites to note the effect of refraction. We then investigate connections between the directional characteristics of the waves at the sites and that of the local wind, concentrating on the origin cases. This will serve as a means to determine the influence of wind on the waves relative to that of refraction. (We note here that, because of the high degree of spatial variability, we do not include the case for subsampled bathymetry here).

Fig. 8.
Fig. 8.

The locations selected for investigation.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

Fig. 9.
Fig. 9.

The histograms for Hawar Islands; M: mode from histograms.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

Fig. 10.
Fig. 10.

The histograms for Ras Laffan; M: mode from histograms.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

Fig. 11.
Fig. 11.

The histograms for Doha Port; M: mode from histograms.

Citation: Journal of Atmospheric and Oceanic Technology 33, 1; 10.1175/JTECH-D-15-0066.1

For all seasons, Ras Laffan always shows a persistent difference between origin and noRefc, primarily due to the wave refraction. Most waves traverse along the central axis of the Persian Gulf, perpendicular to the coastlines of the Hawar Island and Doha Port sites but tangential to the location of the Ras Laffan site. For Ras Laffan, southward- propagating waves (270° in SWAN coordinates) arise primarily from wave refraction, the primary cause accounting for the shift in the peak direction relative to that seen in the noRefc case. Compared to the other sites, the most consistent can be found at Ras Laffan, particularly in the winter and the summer shamal seasons in which the peak is almost up to 0.04. The effect of the lack of refraction on the waves at Hawar Island is, in contrast, relatively small. The differences between the peak of the distributions for origin and noRefc are small for all examined seasons. In addition, with the summer shamal, the distribution of angles in the histograms is slightly wider for origin than for noRefc. Waves propagating southward and over the long shelf north of the site would undergo significant refraction effects; as these effects are dependent on wave frequency, it would result in a broader distribution of wave angles than if refraction were not present. At Doha Port, the peak of the distributions also do not show much difference between the origin and noRefc cases for the nonshamal season. The differences in the summer and winter shamal seasons, though, are larger than seen at the Hawar Island site. In addition, the angle distributions appear to be slightly narrower for the winter and summer shamal origin cases at the Doha Port site than at the Hawar Islands site. This is likely due to the effect of winds and fetch-limited conditions at the Doha Port site; this is further discussed later in this section.

On the upwind side of the Qatar Peninsula—that is, the Hawar Island and Ras Laffan sites— largely remains close to 270°, indicating a large population of southward-propagating waves. In particular, at Hawar Island, for example, Fig. 9 shows dominant with strong clustering around this peak. However, waves due to southerly winds in the winter are also apparent and create the second peak (at ) opposite of the primary heading direction. A second peak in the directional distribution at Ras Laffan can also be seen. In contrast, low occurrence frequencies () and very broad distributions at Doha Port can be found in winter; these are even lower than those during nonshamal and summer seasons. One reason is likely due to the strong and persistent winter shamal, generating waves that propagate toward the southeast and do not refract toward the Qatar Peninsula. It can also be seen in Fig. 11 that the shamal season wind speeds at the Doha Port site are lower than they are at the other two sites; from the peak direction, it is apparent that the shamal winds travel over land before reaching the site, likely reducing their strength. This can also cause wave growth at the Doha Port site to be limited by the fetch, as the winds move off the land and back onto the water, and they could also be responsible for the broader distribution of wave angles.

As shown in Fig. 4, the average wind speed is highest during the winter shamal season, followed by the summer shamal and nonshamal seasons. Strong winds in the shamal seasons occur mainly in the northern or central Persian Gulf basin, while during the nonshamal seasons, the wind is more homogeneous over the entire basin. During nonshamal seasons at Ras Laffan and Doha Port, there is a distinct population of waves approaching from the east. For example, at Ras Laffan, as shown in Fig. 10, another peak in the population of mean directions southward directed appears at 180°. Although most of the waves remain southward, they comprise less of the overall total ( only up to 0.02). Similarly, at Doha Port, the site located entirely on the lee side of the Qatar Peninsula, waves during the nonshamal times are entirely from the east, with the maximum occurrence of , as shown in the central column in Fig. 11.

Compared to the winter, the summer shamal season shows different characteristics. Strong winds in summer mainly reside in the northern basin, as shown in Fig. 4c. The maximum wind speed is smaller than in winter and the center of the strong winds is farther north than seen in other seasons. The winds on the east side of the Qatar Peninsula are weaker than they are in winter. Despite the mild easterly winds, there is still a small population of waves arriving from the east at the Ras Laffan and Doha Port sites during the summer shamal season. Both the Ras Laffan and Doha Port show a second peak of distributions near 180°. In particular, the Doha Port site experiences westward-propagating waves that are of comparable occurrence frequency to those propagating southward, despite the relatively weaker easterly winds. This reflects the presence of waves generated over long cross-basin fetch east of Doha Port.

During the nonshamal season at Doha Port, westward-propagating waves comprise the largest population of wave environment in the area (Fig. 11). As with the summer shamal season, there is no apparent correlation between the population of the wind direction and that of the waves, because the wind directional distribution seems almost evenly matched between easterly and northwesterly winds. This is again an indication of remotely generated waves propagating from areas east of Doha Port over the large cross-basin fetch to the east. In contrast, during the nonshamal season, south- and southeast-directed waves are scarce at Doha Port, in line with the small presence of winds from this direction. This serves as further confirmation of the fetch-limited wave-generation conditions for northwesterly winds as they move over the Qatar Peninsula and over water near Doha Port.

5. Conclusions

The bathymetric effects of wind waves for the Persian Gulf have been studied with a 5-yr hindcasting exercise using SWAN. Using a high-resolution wind data source, the spatial and temporal characteristics of the wave climates can be studied via statistics from the numerical results. By deactivating depth-induced refraction and breaking, the run scenarios noRefc and noBrek are generated for comparison to the results from the normal hindcasting scenario origin.

The 5-yr total energy deviation (TED) is calculated for each grid point and plotted as seasonal contour maps, both for noBrek and noRefc. Because of wave breaking TED is in the range of ±2%, mainly distributed in the Strait of Hormuz, behind islands, and the nearshore regions. Depth-induced wave breaking in the main basin is geographically scattered. Patterns of positive TED in the Strait of Hormuz during the nonshamal season can be due to smaller waves overall during this time, amplifying TED. During this same season, a large area of negative TED is seen near the Gulf of Oman, which may be due to higher waves in the noBrek case experiencing higher whitecapping dissipation. On the other hand, TED due to refraction (noRefc) is ±20%, an order of magnitude larger than that due to breaking (noBrek). In addition to the areas where refraction is expected to be important—for example, behind islands and the nearshore regions—nonzero TED due to refraction also can be found in some shallow areas of the main basin, particularly in the southern area (24°–26°N) east of Qatar (51.5–55°E). In contrast to wave breaking, depth-induced refraction is affected by the effect of bathymetry in the offshore region, as well as by the effect of coastlines. In the northeastern corner of Qatar, for example, over 20% TED due to refraction is resolved in the wintertime of all 5 years.

To examine the effect of bathymetry data sensitivity, a comparison case is designed in which all configurations are the same as origin but using subsampled (by a factor of 2) bathymetry data. Not surprisingly, both the absolute depth difference percentage contour map (Fig. 6) and the 5-yr TED (Fig. 7) show that the deeper region is less sensitive to the change of bathymetry data, while the nearshore region is more sensitive. The results are consistent for all seasons and the effect of lacking details of bathymetry is therefore believed to be homogeneous across the two alternative scenarios noRefc and noBrek, which does not affect our conclusions.

Additionally, three nearshore sites around the Qatar coastline are selected for investigation into the effect of refraction on the statistics of the mean wave angle and how this is balanced against the effect of wind. While the effect of activating refraction on the wave energy is substantial, it is less evident in the wave direction for two of the three sites, indicating that the effect of wind also plays a role in steering waves. The western site, Hawar Islands, shows unidirectional southward waves without second directional peaks, except for those propagating at in the winter distribution due to southward winds arriving from the northern Persian Gulf basin. Because its shoreline orientation is roughly tangential to the waves arriving from the north, Ras Laffan shows the most consistent wave directions, the largest , and the largest shift in the peak direction due to refraction, with differences between 10° and 20°. The eastern site, Doha Port, is generally under a fetch-limited condition for northwesterly winds, resulting in smaller and broader distributions in the winter. In addition, there are two distinct peaks in the summer distributions, primarily due to strong winds in summer being situated in the northern area, while weaker winds are present in the area east of Qatar Peninsula. This allows remotely generated waves to propagate toward Doha Port from the east, despite a relatively small population of weak easterly winds at the site. Overall, this study shows the influence of bathymetrically induced effects of refraction and breaking on the distribution of wave energy in the gulf. While these effects are generally important, their importance is not universal, as much of the central region of the Persian Gulf basin shows no difference due to the deactivation of these effects in the SWAN model. In addition, the effect of wind and fetch-limited generation can offset the effect of refraction (or lack thereof), as seen in the wave angle distributions at the two eastern sites (Ras Laffan and Doha Port).

In conclusion, understanding the effect of shamals on the wind waves in Persian Gulf is important for the energy industry. Compared to recent studies, this work is the first to employ the high-resolution COAMPS wind field, as well as long-term hindcasting, to quantitatively characterize the wind-wave seasonal and spatial features due to bathymetric effects, both globally for entire Persian Gulf and locally for Qatar Peninsula. Considering the absence of in situ measurements of wind waves in this area, the results from this work may be useful for operational planning and field experiment design.

Acknowledgments

This work was supported by the Qatar National Research Fund (a member of the Qatar Foundation) under Grant NPRP 5-543-2-220. The authors wish to acknowledge the assistance of Dr. Reza Sadr of the Department of Mechanical Engineering at Texas A& M University at Qatar. The authors are also indebted to Ms. Pamela G. Posey, Oceanography Division, Naval Research Laboratory at Stennis Space Center, Mississippi, for providing the COAMPS hindcast wind fields.

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