Numerical Prediction of Background Buildup of Salinity Due to Desalination Brine Discharges into the Northern Arabian Gulf

: Brine discharges from desalination plants into low-ﬂushing water bodies are challenging from the point of view of dilution, because of the possibility of background buildup e ﬀ ects that decrease the overall achievable dilution. To illustrate the background buildup e ﬀ ect, this paper uses the Arabian (Persian) Gulf, a shallow, reverse tidal estuary with only one outlet available for exchange ﬂow. While desalination does not signiﬁcantly a ﬀ ect the long-term average Gulf-wide salinity, due to the mitigating e ﬀ ect of the Indian Ocean Surface Water inﬂow, its resulting elevated salinities, as well as elevated concentrations of possible contaminants (such as heavy metals and organophosphates), can a ﬀ ect marine environments on a local and regional scale. To analyze the potential e ﬀ ect of background salinity buildup on dilutions achievable from discharge locations in the northern Gulf, a 3-dimensional hydrodynamic model (Delft3D) was used to simulate brine discharges from a single hypothetical source location along the Kuwaiti shoreline, about 900 km from the Strait of Hormuz. Using nested grids with a horizontal resolution, comparable to a local tidal excursion (250 m), far ﬁeld dilutions of about 28 were computed for this discharge location. With this far ﬁeld dilution, to achieve a total dilution of 20, the near ﬁeld dilution (achievable using a submerged di ﬀ user) would need to be increased to approximately 70. Conversely, the background build-up means that a near ﬁeld dilution of 20 yields a total dilution of only about 12.


Introduction
Marine impacts associated with brine discharge are mainly judged on their brine and contaminant concentrations after initial mixing (dilution). Dilution is generally obtained through judicious choice of outfall parameters, including location, orientation, number of ports, discharge flow rate, etc., using a combination of analytical and physical models. The effectiveness of any discharge design will depend on the relative magnitude of the near and far field dilution. In general, the near field is facilitated by turbulent entrainment processes, while the far field is dominated by advection and diffusion processes.
The far field dilution is defined as: where c o , c a , and c F are the pollutant concentrations in the discharge, the ambient (water not influenced by the discharge) and the far field (region >~100 meters surrounding the discharge), and the near field dilution is defined as: where c N is the concentration in the near field (<~100 meters from the source). The combined or total local dilution at a given location, defined as: can be obtained algebraically by combining Equations (1)-(3) to obtain: or approximately the harmonic sum of S N and S F. In addition, over time, it is useful to calculate a harmonic mean far field dilution (after [1,2]), which is equivalent to the arithmetic mean concentration: While recent numerical efforts and computational advances have been able to refine the horizontal resolution to 10s of meters (and, therefore, reduce the distance between the near and far field), multiport diffusers with port diameters on the order of 10 cm would require resolutions of sub-meter level resolution, plus additional physics (e.g., entrainment, bubble dynamics or stratification) to properly model the near field mixing processes [3]. It is therefore more computationally economical to adopt two separate models to model the near and far field models and to couple them, to yield an overall dilution that is of interest [4,5].
The primary objective of this paper is to investigate the potential background buildup of a low-flushing water body on a local scale. It begins with a brief description of the oceanographic conditions of the paper's focus area, the Arabian or Persian Gulf (hereafter referred to as the Gulf-a body of water with the potential of increased background buildup), and an analysis of long-term Gulf-wide salinity changes, due to desalination. The study considers a single hypothetical desalination brine discharge, located in the northern Gulf, and present predicted far field dilutions, using a Gulf-wide hydrodynamic model (Delft3D). The paper discusses the importance of the grid resolution, in order to resolve the background buildup concentrations, as well as illustrate tradeoffs which occur when the current fields are not well resolved. Finally, although this paper does not directly provide a diffuser outfall design, it will discuss the impact of the predicted background buildup on the target dilutions, that would need to be accomplished when designing a diffuser outfall.

Case Study: Gulf Scale Environmental Impact
The Gulf is a shallow (mean depth of about 35 m), reverse tidal estuary, with only one outlet available for exchange flow (the Strait of Hormuz), located roughly 1000 km downcoast from the head of the Gulf. It has a minimum width of about 65 km, a maximum width of about 340 km, maximum length of about 990 km, total surface area of 239,000 km 2 , and a total volume of about 9000 km 3 [6,7] ( Figure 1).
The Gulf consistently carries about a third of the world's total seawater and brackish water desalination capacity [8,9]. Desalination has been conducted predominantly via multi-stage flash distillation (MSF) technology since the 1950s, and, due to the heat energy required, this has always been an energy intensive process. MSF plants were often located near power stations, to take advantage of the pre-heated water from the power plants' cooling water stream as feed water for the MSF plant, in order to reduce the overall energy cost of the desalination process. In recent decades, reverse osmosis (RO) has been adopted, because of the reduced cost of desalination and its scalability (it may be implemented for individual buildings up to the largest plant, e.g., Ashkelon, Israel, with a capacity of 320,000 m 3 /day) [10].
Brine discharges from reverse osmosis (RO) desalination plants, located mostly throughout the Arabian coast, can contain excess salinity (up to 35,000 ppm greater than ambient), contaminants, such as heavy metals and organophosphates [9,11]. Discharges from multistage flash desalination plants additionally have an excess temperature, in the range of about 5-15 degrees Celsius warmer than ambient seawater [9].
Several studies on Gulf-wide circulation patterns exist in the literature [6,7,[12][13][14][15][16][17][18][19]. This paper focuses on the drivers of the Gulf-wide circulation that are responsible for observed residual currents at a given location in the northern Gulf. The following section presents the spatial, seasonal and long-term trends in Gulf-wide salinity, which contribute to overall circulation patterns in the Gulf.
(MSF) technology since the 1950s, and, due to the heat energy required, this has al nergy intensive process. MSF plants were often located near power stations, to of the pre-heated water from the power plants' cooling water stream as feed water fo , in order to reduce the overall energy cost of the desalination process. In recent dec osis (RO) has been adopted, because of the reduced cost of desalination and its scala implemented for individual buildings up to the largest plant, e.g. Ashkelon, Israel, w 320,000 m 3 /day) [10]. discharges from reverse osmosis (RO) desalination plants, located mostly throughou ast, can contain excess salinity (up to 35,000 ppm greater than ambient), contamin avy metals and organophosphates [9,11]. Discharges from multistage flash desalin itionally have an excess temperature, in the range of about 5-15 degrees Celsius wa nt seawater [9]. al studies on Gulf-wide circulation patterns exist in the literature [6,7,[12][13][14][15][16][17][18][19]. This p the drivers of the Gulf-wide circulation that are responsible for observed residual cur ocation in the northern Gulf. The following section presents the spatial, seasonal and s in Gulf-wide salinity, which contribute to overall circulation patterns in the Gulf. ide Circulation ualitative description of the circulation pattern in the Arabian Gulf presented here is servations by Reynolds, 1993 andJohns et al. 2003 [6,7]. The Gulf itself is shallower n coast (typically only about 20 m depth) and the Gulf deepens into a trough that the Iranian coast in the north. The bathymetry of the Gulf is very shallow in the sou ith typical bottom slopes of about 4 m over 10 km.

Gulf-Wide Circulation
The qualitative description of the circulation pattern in the Arabian Gulf presented here is based on field observations by Reynolds, 1993 andJohns et al. 2003 [6,7]. The Gulf itself is shallower near the Arabian coast (typically only about 20 m depth) and the Gulf deepens into a trough that runs parallel to the Iranian coast in the north. The bathymetry of the Gulf is very shallow in the southern portion, with typical bottom slopes of about 4 m over 10 km.
The circulation in the Gulf is dominated by the exchange flows in and out of the Strait of Hormuz-see Figure 2. A lower salinity surface current, known as the Indian Ocean Surface Water (IOSW), flows into the Gulf year-round (T 1 in Figure 2), initially flowing northward along the Iranian coast. While a small part of the surface current flows back out along the southern part of the Strait (shown as T 2 in Figure 2), the bulk of the flow intrudes into the Gulf, and mixes with the existing hypersaline water in the Gulf [7]. The prevailing wind, called the Shamal, is from the Northwest, and can have velocities of up to 18 m/s in the winter, compared with less than 10 m/s in the summer [13]. Additionally, the Northern Gulf receives freshwater river inflows along the Iranian coast and at the Shatt al-Arab, which contributes to circulation (with two branches of freshwater flowing southward along the Arabian and Iranian coasts). The intense evaporation of the shallow water from the Northern Gulf and the UAE coast creates a dense brine that spills into the trough to the north and leaves the Strait as a subsurface gravity current (shown as T 3 in Figure 2). Throughout the Gulf, the tide and wind induce shear that is responsible for the dispersion of tracers. Residence times, calculated by Alosairi et al. 2011 [16], for tracer sources within the Gulf, are depicted in Figure 3. Tracer sources in shallow regions of the Arabian coast (e.g. Kuwaiti coast, Bahrain and UAE coasts) may experience residence times of 2 to 3 yrs.

Flow
Annual flow (expressed as equivalent Gulf-wide precipitation rate, m/yr) Throughout the Gulf, the tide and wind induce shear that is responsible for the dispersion of tracers. Residence times, calculated by Alosairi et al. 2011 [16], for tracer sources within the Gulf, are depicted in Figure 3. Tracer sources in shallow regions of the Arabian coast (e.g., Kuwaiti coast, Bahrain and UAE coasts) may experience residence times of 2 to 3 yrs. Throughout the Gulf, the tide and wind induce shear that is responsible for the dispersion of tracers. Residence times, calculated by Alosairi et al. 2011 [16], for tracer sources within the Gulf, are depicted in Figure 3. Tracer sources in shallow regions of the Arabian coast (e.g. Kuwaiti coast, Bahrain and UAE coasts) may experience residence times of 2 to 3 yrs.

Flow
Annual flow (expressed as equivalent Gulf-wide precipitation rate, m/yr)

Gulf-Wide Salinity
Xue and Eltahir, 2015 [21] provided estimates of the Gulf water balance, expressed as a Gulf-averaged precipitation rate (Table 1): Table 1. Gulf water balance (Based on [21]). Desalination up to −0.04 m/yr (may be smaller in magnitude, due to the return of some of the freshwater back into the Gulf after domestic/industrial use) [22] As seen above, on a basin-wide basis, desalination amounts to an equivalent of about 2% of the evaporative loss of freshwater from the Gulf, and thus is not a major contributor to freshwater loss or increased salinity. The salinity of the Gulf is typically about 38-42 practical salinity units (psu), and it is clear from the water balance above that the high salinity of the Gulf is due to its large evaporation output compared with river and rain inputs.

Flow Annual Flow (Expressed as Equivalent Gulf-Wide Precipitation Rate, m/yr)
Salinity values taken at different locations over the Gulf over the period 1955-2012 were obtained from the World Ocean Atlas ( [19]; statistical mean of temperature on 1/4 • grid). Figure 4 shows that the interdecadal variability of the salinity in the Gulf is less than the seasonal variability. The lack of variability over the decades could be attributed to the mitigating effect of the fresher inflows from the Indian Ocean via the Hormuz strait, as confirmed by modeling studies on Gulf equilibria conditions by Ibrahim, 2017 [19]. As observed on a smaller scale between two bodies of water of differing density, separated by a narrow slot (analogous to the narrow Hormuz strait) [23], the larger the density difference between the two water bodies, the larger the magnitude of the mitigating exchange flow.
Water 2019, 11, x FOR PEER REVIEW 5 of 14 As seen above, on a basin-wide basis, desalination amounts to an equivalent of about 2% of the evaporative loss of freshwater from the Gulf, and thus is not a major contributor to freshwater loss or increased salinity. The salinity of the Gulf is typically about 38-42 practical salinity units (psu), and it is clear from the water balance above that the high salinity of the Gulf is due to its large evaporation output compared with river and rain inputs.
Salinity values taken at different locations over the Gulf over the period 1955-2012 were obtained from the World Ocean Atlas ( [19]; statistical mean of temperature on 1/4° grid). Figure 4 shows that the interdecadal variability of the salinity in the Gulf is less than the seasonal variability. The lack of variability over the decades could be attributed to the mitigating effect of the fresher inflows from the Indian Ocean via the Hormuz strait, as confirmed by modeling studies on Gulf equilibria conditions by Ibrahim, 2017 [19]. As observed on a smaller scale between two bodies of water of differing density, separated by a narrow slot (analogous to the narrow Hormuz strait) [23], the larger the density difference between the two water bodies, the larger the magnitude of the mitigating exchange flow.

Delft3D model
This paper used a 3-dimensional finite difference hydrodynamic model, coupled with a water quality module (Delft3D-FLOW) [25,26], as a tool to determine the far field dilution of various contaminants, as well as to quantify a background far field concentration that may affect near field outfalls. The basis for this model was the Gulf Community Model (see www.agmcommunity.org), which has been adjusted for use in the current study. A combination of measured bathymetry data, meteorological and tidal forcings, as well as freshwater riverine inflows into the Gulf, were input into the model to simulate circulation patterns in the Gulf. Details of the model are presented below.
The basic Arabian Gulf Model used a 4 km square grid (lat/lon) plus 10 vertical sigma layers

Delft3D Model
This paper used a 3-dimensional finite difference hydrodynamic model, coupled with a water quality module (Delft3D-FLOW) [25,26], as a tool to determine the far field dilution of various contaminants, as well as to quantify a background far field concentration that may affect near field outfalls. The basis for this model was the Gulf Community Model (see www.agmcommunity.org), which has been adjusted for use in the current study. A combination of measured bathymetry data, meteorological and tidal forcings, as well as freshwater riverine inflows into the Gulf, were input into the model to simulate circulation patterns in the Gulf. Details of the model are presented below.
The basic Arabian Gulf Model used a 4 km square grid (lat/lon) plus 10 vertical sigma layers ( Figure 5). Our model used a 4-year hydrodynamic spin-up with a time step of 5 minutes, because contaminants discharged at Kuwait Bay may take 3 years to exit the Gulf. External forcings include gridded wind and meteorological data, and four river inputs. Tidal forcings (expressed as a time series of water elevations) were imposed along the external boundary, a transect across the Gulf of Oman in the southeastern edge of the domain (shown in Figure 5). A bottom roughness (Manning's coefficient n = 0.03) was used throughout the Gulf.

Current Speed Calibration
As the study focuses on the northern Arabian Gulf, close to Kuwaiti waters, the modeled velocity was compared with available water elevation time series at one grid cell location (Umm al Maradim Island) with Acoustic Doppler Current Profiler (ADCP) measurements provided by the Kuwait Institute of Scientific Research (KISR), during the summer of 2011, for a location ~ 25 km offshore and ~ 90 km south of Kuwait City; 28 deg 40.153'N, 48 deg 38.760'E, [25]. This data provided a sense of the tidal conditions present near the Southern Kuwaiti shore, as well as data for model calibration. Figure 6 shows a good comparison between the measured current speeds (eastward and northward) and the Delft3D modeled speeds. The observed current is mainly tidal in the southeast and northwest directions, consistent with the shore parallel direction. There is also a mean residual current of 4 cm/s in the south-southeast direction (bearing about 170 degrees). As shown in Figure 6, there is a slight mismatch in the orientation of the currents, which could be a result of the current meter's location near an island (of dimension 800 by 300 m), whose bathymetry may not be resolved from the available depth data and model grid resolution (250 m).
While monthly data were available for some dissolved chemicals (KEPA, personal communication, 2017) for about 13 onshore and offshore locations, the time resolutions (one reading a month) are insufficient to be useful for purposes of model calibration or validation. Additionally, the monitoring locations may experience contaminants originating from multiple sources along the

Current Speed Calibration
As the study focuses on the northern Arabian Gulf, close to Kuwaiti waters, the modeled velocity was compared with available water elevation time series at one grid cell location (Umm al Maradim Island) with Acoustic Doppler Current Profiler (ADCP) measurements provided by the Kuwait Institute of Scientific Research (KISR), during the summer of 2011, for a location~25 km offshore and~90 km south of Kuwait City; 28 • 40.153 N, 48 • 38.760 E, [25]. This data provided a sense of the tidal conditions present near the Southern Kuwaiti shore, as well as data for model calibration. Figure 6 shows a good comparison between the measured current speeds (eastward and northward) and the Delft3D modeled speeds. The observed current is mainly tidal in the southeast and northwest directions, consistent with the shore parallel direction. There is also a mean residual current of 4 cm/s in the south-southeast direction (bearing about 170 degrees). As shown in Figure 6, there is a slight mismatch in the orientation of the currents, which could be a result of the current meter's location near an island (of dimension 800 by 300 m), whose bathymetry may not be resolved from the available depth data and model grid resolution (250 m).
While monthly data were available for some dissolved chemicals (KEPA, personal communication, 2017) for about 13 onshore and offshore locations, the time resolutions (one reading a month) are insufficient to be useful for purposes of model calibration or validation. Additionally, the monitoring locations may experience contaminants originating from multiple sources along the Kuwaiti coastline, which again cannot be resolved with the space and time resolutions available. The model calibration, using tidal data, is discussed in the section below.  Figure 6. (a) Northward and eastward velocities measured by the ADCP at 10 m depth (same current meter as [21]; red) and depth averaged predictions by Delft3D for the same times (blue), (b) longshore velocities: Delft3D predictions (blue) versus measured velocities (red).

Tidal Response Calibration
While matching current speeds is an important aspect of calibration, it is also important for the model to match the tidal response at the Gulf scale. Figure 7 shows the locations in the Gulf with tidal gage data available as harmonic components. Figure 8 shows the correlation plots of M2, K1, O1, and S2 tidal components for amplitude and phases, compared with those modeled by the calibrated Delft3D model. These show that the Gulf-wide Manning's friction coefficient of = 0.03 has resulted in good agreement with the Gulf-wide tidal amplitudes, The Gulf-wide modeled and observed tidal phases were mostly in agreement.  [21]; red) and depth averaged predictions by Delft3D for the same times (blue), (b) longshore velocities: Delft3D predictions (blue) versus measured velocities (red).

Tidal Response Calibration
While matching current speeds is an important aspect of calibration, it is also important for the model to match the tidal response at the Gulf scale. Figure 7 shows the locations in the Gulf with tidal gage data available as harmonic components. Figure 8 shows the correlation plots of M2, K1, O1, and S2 tidal components for amplitude and phases, compared with those modeled by the calibrated Delft3D model. These show that the Gulf-wide Manning's friction coefficient of = 0.03 has resulted

Hormuz Strait Calibration
The Delft3D model was run for the entire year of 2010, and was used to compute temperature and salinity along the cross section (Figure 9), as well as the flux out of the Hormuz Strait, at different months ( Figure 10). Figure 10 compared the model results with those predicted by [19], using another numeric model, FVCOM. The behavior shown in Figures 9 and 10 corroborates with the qualitative circulation behavior reported by [8], namely: (1) the increased salinity stratification, coupled with influx of fresher water into the Gulf during February, and (2) the outflow of saltier water along the surface, as well as in the deeper part of the strait, in October (consistent with the flow pattern shown in Figure 2).
Water 2019, 11, x FOR PEER REVIEW 9 of 14

Hormuz Strait Calibration
The Delft3D model was run for the entire year of 2010, and was used to compute temperature and salinity along the cross section (Figure 9), as well as the flux out of the Hormuz Strait, at different months ( Figure 10). Figure 10 compared the model results with those predicted by [19], using another numeric model, FVCOM. The behavior shown in Figures 9 and 10 corroborates with the qualitative circulation behavior reported by [8], namely: (1) the increased salinity stratification, coupled with influx of fresher water into the Gulf during February, and (2) the outflow of saltier water along the surface, as well as in the deeper part of the strait, in October (consistent with the flow pattern shown in Figure 2).   Positive fluxes (red) represent flow out of the Gulf. Top row indicates Ic1, the high-salinity equilibrium attained by a high initial conditions of salinity (Gulf-wide salinity = 40 g/kg), predicted by FVCOM model (from [19]). Middle row indicate Ic2, the low-salinity equilibrium attained by low initial conditions for salinity (Gulf-wide salinity = 25 g/kg) predicted by [19]. Bottom row indicates model predictions from the current Delft3D model.

Nested Models
The calibrated Delft3D model was used to investigate the effect of horizontal grid resolution on the predicted far field dilution near a hypothetical brine discharge, located close to the Al-Zour power plant (a source of desalination brine). The location was chosen as it was a coastal region, close to the current meter data; similarly, the model time period matched that of current meter observations (March 2010). Figure 11(a) shows the inner nested model grids, in relation to the outer model. The model's horizontal resolution was increased in the area offshore of the southern coast of Kuwait, Positive fluxes (red) represent flow out of the Gulf. Top row indicates Ic1, the high-salinity equilibrium attained by a high initial conditions of salinity (Gulf-wide salinity = 40 g/kg), predicted by FVCOM model (from [19]). Middle row indicate Ic2, the low-salinity equilibrium attained by low initial conditions for salinity (Gulf-wide salinity = 25 g/kg) predicted by [19]. Bottom row indicates model predictions from the current Delft3D model.

Nested Models
The calibrated Delft3D model was used to investigate the effect of horizontal grid resolution on the predicted far field dilution near a hypothetical brine discharge, located close to the Al-Zour power plant (a source of desalination brine). The location was chosen as it was a coastal region, close to the current meter data; similarly, the model time period matched that of current meter observations (March 2010). Figure 11a shows the inner nested model grids, in relation to the outer model. The model's horizontal resolution was increased in the area offshore of the southern coast of Kuwait, based on the description of potential adverse effects to the marine environment, shown in Figure 11a, below. The three nested grid levels used were as follows: based on the description of potential adverse effects to the marine environment, shown in Figure  11(a), below. The three nested grid levels used were as follows: • Outer = ~4 km grid (0.05 degrees)-entire Gulf • Mid = ~1 km grid (0.01 degrees), offshore of Kuwait to ~40 km • Fine = ~500 m grid (0.005 degrees), offshore of Kuwait to ~25 km • Finest = 250 m grid (0.0025 degrees), offshore to Kuwait to ~10 km Using the model results from the three nested grids, it is possible to test the mesh sensitivity of the computed dilution, resulting from a source shown in Figure 11(b). To do this, model-predicted concentration timeseries were obtained for the following locations (shown in Figure 11 Using the model results from the three nested grids, it is possible to test the mesh sensitivity of the computed dilution, resulting from a source shown in Figure 11b. To do this, model-predicted concentration timeseries were obtained for the following locations (shown in Figure 11b):

1.
Locations~4 km away (horizontal grid resolution of the outer model), shown in red; 2.
Locations~1 km away (resolution of the mid-scale model), shown in green; 3.
Locations~500 m away (resolution of the fine model), shown in blue; and 4.
Locations~250 m away (resolution of the finest model), shown in yellow. Table 2 shows the harmonic time-averaged dilutions (defined in Equation (5)) computed at the various locations indicated in Figure 11b, using each of the nested model outputs. Harmonic mean dilution values, at locations that are subgridscale for a particular nested model, were spatially interpolated (shown in the table with grey shading). It can be seen in Table 2 that the predicted dilutions are sensitive to the horizontal resolution. For locations within~250 m from the source (from the finest resolution model), the model predicted lower far field dilution ( S F ∼ 14 − 59, with a harmonic average of 28). With a near field dilution of S N = 20, this harmonic average far field dilution (computed using Equation (5)) would result in a total dilution 1 S T = 1 S F + 1 S N , of about S T = 12. It is worth noting that there is a balance between the flow field resolution and the predicted dispersion. This was explored by [27], using a reverse Gaussian puff model [28] which simulates the discharge over multiple tidal cycles, using puffs of conservative contaminant that grow in size, according to [29]. The model used a constant depth equal to the local depth of 3 m at the yellow points indicated in Figure 11b, and assumed a spatially unvarying flow field (that has a similar effect to using a coarser grid for velocities). The Gaussian puff model's assumption of a spatially uniform velocity under-predicted the dilutions, and only matched the Delft3D predictions when the puff model diffusivity was increased by a factor of about 1.5, compared with the value prescribed by [28]. This difference may be attributed to the puff model's use of a simplified flow field, while the Delft3D model exhibits a higher dispersion of the contaminant plume by capturing the spatial variation in the velocity field.
The far field (background) buildup has significant implications for near field diffuser design. For a discharge excess salinity of ∆S ∼ 40 and a target excess salinity of ∆S ∼ 2, a total dilution of S T ∼ 20 is required [3]. With zero background buildup, a near field dilution of S N ∼ 20 would suffice. However, the modeling result here indicates that S F ∼ 28, and, in order to achieve a total dilution of S T ∼ 20, the near field dilution would now need to be S N ∼ 70.
Other water bodies have far higher flushing potential for contaminants than the Gulf. For example, brine discharges from an outfall from a desalination plant sited in Tuticorin, along the southeastern Indian coast, are expected to observe a dilution of over 1600 within less than 1 km downstream of the outfall [30]. Desalination discharges from nearby Omani desalination plants, situated on the coastline of the Gulf of Oman, are also able to be diluted by a factor of 35-100 at about 50 m downstream of the discharge, and over 2000 about 2 km downstream [10].

Conclusions
Far field dilutions were computed using the Delft3D model, at about one tidal excursion from the source, as a measure of the background concentrations experienced by the source in an offshore discharge location in the northern Arabian Gulf. By comparing the results of nested models at different horizontal resolutions, it was determined that the far field dilutions are only accurately captured when the Delft3D horizontal resolution is on the order of the tidal excursion. Also, the computed harmonic mean dilutions for the far field approach near field dilutions ( S N ∼ 20), indicating that far field contaminants do "double back" at the source, and near field diffusers would have to be designed to produce higher dilutions to satisfy target total dilutions. A higher/lower brine discharge, coupled with smaller/larger tidal excursions and smaller/larger residual velocities, would result in a smaller/larger far field (background) dilution.