Evaluating the eutrophication risk of artificial lagoons–case study El Gouna, Egypt

Eutrophication problem in El Gouna shallow artificial coastal lagoons in Egypt was investigated using 2D TELEMAC-EUTRO-WAQTEL module. Eight reactive components were presented, among them dissolved oxygen (DO), phosphorus, nitrogen, and phytoplankton biomass (PHY). The effect of warmer surface water on the eutrophication problem was investigated. Also, the spatial and temporal variability of the eutrophication was analyzed considering different weather conditions: tide wave, different wind speeds and directions. Moreover, effect of pollution from a nearby desalination plant was discussed considering different pollution degrees of brine discharge, different discharge quantities and different weather conditions. Finally, new precautions for better water quality were discussed. The results show that tide wave created fluctuations in DO concentrations, while other water quality components were not highly influenced by tide’s fluctuations. Also, it was found that high water temperatures and low wind speeds highly decreased water quality producing low DO concentrations and high nutrients rates. High water quality was produced beside inflow boundaries when compared to outflow boundaries in case of mean wind. Moreover, the results show that the average water quality was not highly deteriorated by the nearby desalination operation, while the area just beside the desalination inflow showed relatively strong effects. Different weather conditions controlled the brine’s propagation inside the lagoons. Moreover, increasing the width of the inflow boundaries and injecting tracer during tide and mean wind condition are new precautions which may help to preserve the water quality in a future warmer world. This study is one of the first simulations for eutrophication in manmade lagoons.


Introduction
The water eutrophication problem is considered one of the most challenging environmental issues resulting in destructive effects on aquatic ecosystems (Pal, 2020). It means the enrichment of the water bodies with excess components of nitrogen (N) and phosphorous (P), which cause oxygen depletion problems (Yang et al., 2008). Eutrophication leads to the degradation Abstract Eutrophication problem in El Gouna shallow artificial coastal lagoons in Egypt was investigated using 2D TELEMAC-EUTRO-WAQTEL module. Eight reactive components were presented, among them dissolved oxygen (DO), phosphorus, nitrogen, and phytoplankton biomass (PHY). The effect of warmer surface water on the eutrophication problem was investigated. Also, the spatial and temporal variability of the eutrophication was analyzed considering different weather conditions: tide wave, different wind speeds and directions. Moreover, effect of pollution from a nearby desalination plant was discussed considering different pollution degrees of brine discharge, different discharge quantities and different weather conditions. Finally, new precautions for better water quality were discussed. The results show that tide wave created fluctuations in DO concentrations, while other water quality components were not highly influenced by tide's fluctuations. Also, it was found that Vol:. (1234567890) of cultural and social values of polluted water bodies. For instance, large hypoxic or dead zones are formed in high polluted ecosystems, which result in the reduction of fish and shellfish production (Wurtsbaugh, 2019). Also, coral reefs are highly stressed and decline affected by eutrophication (Kroon et al., 2016). Up to 2012, the Fifth Global Environment Outlook (GEO-5) stated that more than 40% of the total world water bodies suffer from eutrophication. This environmental crisis has become a vital social issue involving a wide variety of stakeholders aiming at eutrophication reduction (Smetacek & Zingone, 2013). In North America and Europe, there are great successes in reducing the problem; however, many developing countries still suffer from lots of water eutrophication problems (Wurtsbaugh, 2019).
Nowadays, eutrophication problems are being increased affected by both anthropogenic activities and natural phenomena. For instance, the increasing anthropogenic activities such as agricultural, recreational and industrial interests, fossil fuel combustion, and many other economic growth activities are dramatically increasing aquatic nitrogen and phosphorus pollution (Wurtsbaugh, 2019). On the other hand, most water bodies are naturally negatively affected by a gradual slow process of nutrient enrichment as they age affected by sediments and algal decomposition. The geomorphology, mean water depth, wind, and tide are considered major natural hydrodynamic factors affecting eutrophication (de Jonge et al., 2002). Moreover, the expected natural climate change in the upcoming decades will also have direct and indirect effects on water eutrophication considering changes in metrological factors such as water temperature, precipitation patterns, solar radiation, and wind effects (Woznicki et al., 2016;Xia et al., 2016). For instance, the water temperature is considered a major environmental factor affecting water quality parameters such as algal bloom stimulation and increase of nutrients (Nazari-Sharabian et al., 2018). In a globally warming climate, air temperature is expected to increase by 1.1-6.4 °C by 2100, which, in turn, rapidly increases water temperature (Anthony et al., 2009). Also, any decrease in wind speeds can increase algae production and hinder the release of nutrients from sediments (George et al., 2007). In the expected climate change, the wind speeds are tending to decrease (with a negative effect on water quality) or increase (with a positive effect on water quality) affected by global warming depending on the studied location (Eichelberger et al., 2011).
In the last decades, researchers began to focus on the effect of the upcoming climate change and natural phenomena on the water quality and the eutrophication problem using field investigations or numerical models, which are widely accepted in complex domains such as coastal areas. For instance, Kim et al., (2018), Liu et al. (2019), Sepulveda-Jauregui et al. (2018), and Trombetta et al. (2019) investigated the effect of increasing water temperature on different water quality parameters. They found out that increasing water temperature played a major role in reducing water quality in water systems. Also Deng et al. (2018), Kunarso et al. (2018), Marlina and Melyta (2019), Morgan et al. (2019), Wirasatriya et al. (2018), and Zhang et al. (2017) studied the effect of different wind speeds on water eutrophication problems. They found out that decreasing wind speed can increase water pollution, e.g., the decrease of dissolved oxygen (DO) concentrations and the increase of water pollutants of phosphorus and nitrogen. Moreover, Fatema et al. (2016), Gasim et al. (2015), and Purnaini et al. (2018) investigated the high effect of tidal waves as a main meteorological parameter on water quality in different water systems.
In particular, eutrophication in coastal water areas is a common phenomenon, which needs more special awareness for many reasons. For instance, coastal areas are destinations for approximately 45% of the human population, which placed these systems under severe anthropogenic stress affected by the increasing nutrient enrichment from unprecedented agricultural, industrial, and urban growth (Kay & Alder, 2005;Wurtsbaugh et al., 2019). Also, coastal areas are more vulnerable to global warming than open estuaries, in which water temperature increases more rapidly reaching approximately four times greater than that of the ocean (Anthony et al., 2009;Nixon et al., 2004). Moreover, coastal areas have complex physical processes with the complexity of describing eutrophication processes affected by their transitional locations (Fernández et al., 2012). Consequently, efficient and effective management of water eutrophication in coastal areas is a challenge considering their societal importance, increasing number of polluted coasts, high population and pollution, high effect of global warming and their complex interactions. Nevertheless, the issue of eutrophication problem in coastal areas, estuaries, and lagoons has attracted less attention from the scholarly community, when compared to lakes investigations (Wurtsbaugh, 2019). More particular, few articles were published considering water pollution in lagoons compared to other coastal areas and estuaries (Ménesguen & Lacroix, 2018). Moreover, to the authors' knowledge, no previous studies investigated the eutrophication problem in manmade lagoons.
In this work, a two-dimensional numerical model using the EUTRO-WAQTEL module of the TELEMAC-2D modeling system was applied for artificial coastal lagoons in El Gouna City located in Egypt. El Gouna's artificial lagoons are connected to the Red Sea and present a touristic and economic environment in Egypt. The lagoons are getting stressed day by day affected by touristic wastes, sewage outflow from lots of hotels, boat leakage, and the outflow from an adjacent desalination plant. Investigation of the hydrodynamics and water quality of El Gouna artificial lagoons has attracted consideration since 2018. Al-Jabari (2018) carried out a field investigation for bathymetry and tide wave affecting the lagoons (Al-Jabari, 2018). Moreover, Abouelsaad et al. (2022a) studied the hydrodynamics of El Gouna lagoons under different weather conditions and tracer transport scenarios. They found that the hydrodynamics of the lagoons were highly affected by the surrounding weather conditions of tide and wind. Also, Abouelsaad et al. (2022b) applied the simple water quality module of TELEMAC-O 2 -WAQTEL for the simulation of DO concentration under different temperatures and weather conditions. They also discussed the negative effect of binary effluents from the nearby desalination plant on DO in the lagoons. O 2 -WAQTEL module is a simple approach, which investigates only DO, organic load (L), and ammoniacal load (NH 4 ) without the full complexity of the manifold biological interactions and feedbacks. Herein, the authors tended to apply the more complicated and more advanced EUTRO-WAQTEL module. The EUTRO-WAQTEL module can be applied to investigate the oxygenation of any water body and is not restricted to modeling reaeration and the global oxidizable load.
The advanced eutrophication module of EUTRO-WAQTEL was used to model phytoplankton biomass (PHY) represented by ChlA, DO, nitrogen (N), and phosphorous (P) in the lagoons. To the authors' knowledge, this study is the first published application of the EUTRO-WAQTEL-TELEMAC module for simulating the eutrophication problem in water systems such as the lagoons in El Gouna. The model provides a spatial and temporal simulation of the eutrophication problem considering the domain hydrodynamics driven by tide, wind, and the lagoons' connection with the Red Sea and the nearby desalination plant. The aim of this work is investigating the eutrophication problem in the lagoons. Firstly, a sensitivity analysis of nine input parameters in the EUTRO-WAQTEL model was carried out discussing their effect on water quality. Afterwards, the effect of different weather conditions on the physical, chemical, and biological characteristics of water was analyzed such as the tide wave, the wind speed, and the wind direction. Also, the expected climate changes of the predicted high temperatures and low wind speeds on water quality were investigated owing to the definite tendency toward lowering the strength of wind speed in the Red Sea.
On the other hand, this study sheds new light on the effect of desalinated water on the eutrophication problem in the receiving coastal lagoons. In this regard, the negative effect of pollution from the nearby desalination plant on the eutrophication process in the lagoons was investigated considering different weather conditions and different pollution intensity of desalination's effluent. Moreover, new precautions or changes in the hydraulics and the operation system of the nearby desalination plant have been discussed for the preservation of the desired water quality in the studied lagoons aiming for better dealing with the surrounding industrial and economical revolution and the expected climate change in the future.

Study area
El Gouna city is located 20 km north of Hurghada City, the capital of the Red Sea governorate in Egypt (see Fig. 1a). It is considered one of the most significant tourist attraction sites in Egypt enriched by tourism activities. El Gouna has a system of artificial lagoons, which were constructed for touristic purposes. The studied domain consists of two connected artificial lagoons with a perimeter of approximately 5000 m and a surface area of 230,000 m 2 with a mean water depth of not more than 2.7 m (see Fig. 1c). Those lagoons are highly stressed by the sewage outflow of touristic hotels, domestic wastes, and boat leakage (Abouelsaad et al., 2022a). The lagoons exchange their water with the Red Sea through three narrow water inlets. Moreover, as the whole city strongly depends on the desalination of salted water through three desalination plants, one nearby desalination plant throws its effluents into the lagoons and is considered the fourth temporary water inlet. Figure 1c shows the four mentioned boundaries with the Red Sea and the desalination plant. The blue ovals represent Dirichlet boundary conditions for water levels of boundaries connected to the Red Sea and the red oval represents the tracer's discharge and concentration from the nearby desalination plant assigned also as Dirichlet boundary conditions.
In 2018, Al-Jabari (2018) draws a picture of the importance of the studied artificial lagoons in El Gouna by studying their bathymetry and tide data. He tracked the water depths for approximately 1700 locations in the whole lagoons. Water depths were not more than 2.7 m. Also, he simulated the tide force affecting the lagoons, which was simulated as a sinusoidal wave, in which every tide wave had an amplitude of 0.6 m every half-day. Since 2013, records of wind speeds and directions have been recorded by the metrological station beside the Technische Universität Berlin Campus El Gouna every 10 min for the whole day. The weighted monthly average wind speed and direction for two years from 2015 to 2017 were calculated to range from 4 to 8.24 m/s with an average value of 5.84 m/s from the northwest direction. Also, the maximum wind speed was found to equal 20.8 m/s blowing from the southeast (Abouelsaad et al., 2022a).

TELEMAC EUTRO-WAQTEL model
For a proper water quality simulation, the water depths and vertically averaged velocity variations must be accurately investigated. In this regard, TELEMAC-2D numerical module was firstly applied to analyze the shallow water flow in the studied lagoons. The shallow water governing equations are the continuity equation, the momentum equations in x-and y-directions and finally the tracer equation (Hervouet & Ata, 2017). Also, Flather's approach (Flather, 1976) was considered to simulate the wind shear stress. TELEMAC-2D was then coupled with EUTRO-WAQTEL module for investigations of water quality. EUTRO-WAQTEL module gives a comprehensive insight into the oxygenation of water by computing the oxygen reaeration and the overall oxidizable load. Moreover, it takes into account the effect of planktonic plant photosynthesis and models the nitrogenous and phosphorus nutrients and their effect on phytoplankton. EUTRO module requires setting the values of more than 25 parameters to simulate eight tracers: PHY defined as the equivalent ChlA concentration, DO, dissolved mineral phosphorus assimilable by phytoplankton (PO 4 ), degradable phosphorus not assimilable by phytoplankton (POR), dissolved mineral nitrogen assimilable by phytoplankton (NO 3 ), degradable nitrogen that cannot be assimilated by phytoplankton (NOR), ammoniacal load assimilable by phytoplankton (NH 4 ), and organic load (L) (Hervouet & Ata, 2017). The tracer conservation equation is given as follows (Hervouet & Ata, 2017): where c is the tracer concentration (mg/l or μg/ l), u and v are the velocity components in x-and y-directions, respectively (m/s), v t,t is the turbulent diffusivity (m 2 /s), F i is a source or sink accounting for water quality interactions of the respective tracer i (mg/l/s).
The eight variables are combined in four interacting systems introduced in the following phytoplankton kinetics, nitrogen cycle, phosphorus cycle, and DO balance.

Phytoplankton kinetics
Phytoplankton mainly consists of unicellular algae that live in water and play a basic role in the food chain. It absorbs mineral elements such as nitrogen, phosphorus, and iron and transforms these materials into organic matter using the light energy received by the chlorophyll they contain via the photosynthesis process (Chao et al., 2010). The governing equation for phytoplankton considering its production and losses is: where F PHY is the phytoplanktonic biomass, CP and DP are algal growth and disappearance rates in (1/day).
The growth rate of a phytoplankton population is a physiological process often limited by temperature, nutrients and light, as shown in Eqs. (3) and (4) (Guildford & Hecky, 2000;Örnólfsdóttir et al., 2004;Wu et al., 2009): (1) where C max is the maximum growth rate (1/day), g 1 is the temperature effect on algal growth (-), μ (lim (phosphate, nitrate)) is the growth limited by the availability of either phosphate, PO 4 , or the sum of nitrate, NO 3 , and ammonium, NH 4 (-), K r1 represents the effect of sunlight on algal growth (-), 1 is the water toxicity coefficient for algae which equals to 1 in the presence of toxicity (-), KP is the half-saturation constant of phosphate (mgP/l), and KN is the half-saturation constant of nitrate (mgN/l).
In the EUTRO-WAQTEL module, the light limitation may be simulated by a depth-integrated Smith function, which does not represent photoinhibition. Herein, the light limitation was neglected to focus on the phytoplankton dynamics under nutrients.
On the other hand, PHY reduction rate is mainly governed by respiration, natural nonpredatory mortality and zooplankton grazing. In the WAQTEL module, the zooplankton grazing is not included as a separate state variable. Nonpredatory mortality accounts for all algal losses which are not explicitly accounted for such as the grazing term or other loss processes. The following equations describe the phytoplankton death rate (DP) as described in TELEMAC: where RP is the phytoplankton respiration rate (1/ day), MP is the algal disappearance rate due to nonpredatory mortality (1/day), M 1 and M 2 are nonpredatory mortality coefficients, g 2 is the temperature effect on phytoplankton disappearance (= 1.050 T−20 ), 2 is the water toxicity coefficient for algae (-), T is the temperature (°C).

Phosphorus cycle
Phosphorus is considered a persistent and serious ecological problem in the eutrophication process through organic and inorganic phosphorus particles (Liu et al., 2006).
Firstly, inorganic phosphorus is incorporated into the biomass during the phytoplankton growth process, while nonliving organic and inorganic particles are recycled during phytoplankton death and undergo mineralization or bacterial decomposition into inorganic phosphorus before utilization by phytoplankton (Wang et al., 2012). Particulate organic phosphorus settles into the sediment. Organic and inorganic phosphorus are modeled in EUTRO module as follows: where f p is the phosphorus content per PHY (mgP/ mgChlA), d tp is the phosphorus percentage that is assimilable in dead phytoplankton (%), K 320 is the mineralization rate from POR to PO 4 at 20 °C (1/ day), f POR is non-algal organic phosphorus deposition flux (mg/m 2 /s), which equals the rate of sedimentation of non-algal organic phosphorus (W POR ), h is the water depth (m).

Nitrogen cycle
During the nitrogen cycle, three nitrogen variables are considered (Eqs. 9, 10, and 11): NO 3 , NOR, and NH 4 . Firstly, inorganic nitrogen is being incorporated into the biomass during phytoplankton growth process, while nonliving organic and inorganic particles are recycled during the phytoplankton death. Nonliving organic nitrogen undergoes mineralization or bacterial decomposition into inorganic nitrogen before utilization by phytoplankton (Wang et al., 2012). Particulate organic nitrogen settles into the sediment.
where f n is the nitrogen content per PHY (mgN/ mgChlA), K 520 is the nitrification rate at 20 °C (1/ day), d tn is the nitrogen percentage that is assimilable in dead phytoplankton (%), K 620 is the mineralization rate from NOR to NO 3 at 20 °C (1/day), f NOR is non-algal organic nitrogen deposition flux (mg/m 2 s), which equals the rate of sedimentation of non-algal organic nitrogen (W NOR ), and R n is the nitrogen proportion that is assimilated from ammonium (-).

Dissolved oxygen balance
Organic load where f is the amount of oxygen produced by photosynthesis (mgO 2 /l), K 120 is the degradation rate of L at 20 °C (1/day), g 3 is the temperature effect on degradation of L (-), f LOR is the non-algal L deposition flux (mg/m 2 s) which is equal to W LOR , and W LOR is the rate of sedimentation of non-algal L (m/s).

Dissolved oxygen
where n is the quantity of oxygen consumed by nitrification (mgO 2 /mgNH 4 ), K 2 is the gas-exchange coefficient between water and atmosphere at 20 °C (1/ day), g 4 is the temperature effect on reaeration (-), C s is the oxygen saturation concentration (mg/l), and BEN is the benthic oxygen demand (mgO 2 /m 2 /day). Reaeration, as one of the most important parameters affecting DO, is affected by water depth, velocity, the slope of the stream, diffusion coefficient, kinematic viscosity, Froude number, or Reynolds number and the head loss (Haider et al., 2013). In the TELEMAC WAQTEL module, four formulas may be considered in reaeration coefficient calculations at 20 °C considering water depth and velocity: formula of Authority, formula of Owens et al. (De la Presa Owens & Innis, 1999), formula of Churchill et al. (Churchill et al., 1964), and formula of O'Connor and Dobbins (O'Connor & Dobbins, 1958). Also, there is another formula that (12) combines three formulae considering ranges for water depth and flow velocity of each point of the mesh using TELEMAC WAQTEL indicated in TELEMAC manual. For all discussed K 2 formulas, the value of K 2 is inversely proportional to water depth and directly proportional to flow velocity (Abouelsaad et al., 2022b). For the aforementioned formulas, the computed reaeration coefficient is determined at 20 • C . Correction of the temperature variation is considered in the TELEMAC model. The oxygen saturation density of water (C s ) is mainly dependent on the water temperature. TELEMAC WAQTEL offers the two most common formulas to calculate C s : formula of Elmore and Hayes and formula of Montgomery (Richardson et al., 2001).
Also, TELEMAC-2D suggests values of benthic demand ranging from 0.007 to 7 gO 2 /m 2 /day at 20 °C depending on the type of soil and bacteria. Moreover, correlation of the effect of temperature variation on the benthic demand is considered in the simulation using TELEMAC model.

Model parameters
A two-dimensional model for simulating El Gouna lagoons was set up using TELEMAC-2D coupled with EUTRO-WAQTEL module, using an unstructured triangular grid created by Janet mesh generation's program as a part of smile software. A suitable unstructured fine mesh was generated counting in a total of about 2700 nodes and 4800 triangular elements with a mesh resolution, which ensured grid convergence, i.e., changes in model results using a refined grid can be neglected. In TELEMAC-2D simulations, the method of characteristics was applied to solve the shallow water equations by applying linear discretization for the flow velocities and tracer, while the PSI method was used for calculations of water depth. Also, Strickler's law with a magnitude of 40 m 1/3 /s was adopted for the calculation of bottom friction (Abouelsaad et al., 2022a). Finally, a constant initial condition for water elevation of 12 m above the mean sea level and initial zero velocities were initially applied over the entire domain. The prescribed values for cross-section characteristics and numerical schemes were obtained from a previous study carried out by Abouelsaad et al. (2022a).
TELEMAC-2D is then compiled with the EUTRO-WAQTEL module using a separate steering file, which includes the different physical and biochemical processes of the eutrophication problem as illustrated in Eqs.
(2) to (13). The EUTRO module is applied for simulating the eight beforementioned tracers using approximately 25 parameters shown in Table 1. The table indicates the default values of the parameters suggested by the user's manual of TELEMAC. The ranges of some parameters, which were previously discussed by literature research, are also indicated.
Field data about water quality in the studied lagoons are not available. Consequently, the initial background values of the tracers were considered from a previous nearby field study in 2016 (Fahmy et al., 2016) who collected a total of 108 seasonal coastal water samples during the period from 2011 to 2013 to investigate the hydrography, heavy metals, nutrient salts, and petroleum hydrocarbons in the Red Sea. One of their studied regions is relatively near to our lagoons. Table 2 illustrates the initial simulated values of tracers as discussed in the mentioned study.

Simulation scenarios
A sensitivity analysis of the eutrophication problem in the lagoons under the effect of nine different input parameters was firstly carried out using the EUTRO-WAQTEL module for simulations of water quality. The effect of every input parameter was discussed by computing the percental difference (%), which was derived as the difference between the results of water quality parameters corresponding to the maximum and minimum values of the investigated input parameter divided by the minimum simulated values. Although no data for model calibration were available, we could gain an insight into how the water quality is influenced by changes in chosen values and whether the results are in reasonable ranges. In all sensitivity analysis scenarios, the same weather condition of the tide (with an amplitude of 0.6 m two times daily) with the mean wind (5.84 m/s from the northwest direction) was adopted over a period of 6 days. Table 3 illustrates the investigated input parameters, their simulated values and the expected effect on water characteristics.
Further, different weather conditions were investigated considering different tide, wind, and temperature characteristics discussing their effects on the water quality of the studied artificial lagoons. For instance, the influence of three different water temperatures of 20 °C, 25 °C, and 30 °C and the effect of ups and downs resulting from the tide wave were simulated. Also, the effect of different wind speeds ranging from 8.24 to 4.01 m/s blowing from the mean wind direction of 322° (northwest direction) and the maximum blowing wind during the study period with a wind speed of 20.80 m/s from southeast direction was also investigated. Three observation points, shown in Fig. 1c, were chosen   Fig. 1c. Moreover, the effect of the main source of pollution from the nearby desalination plant was simulated. For the following scenarios, beside comparing the average values in the whole domain, point 845 just beside the desalination inflow (shown in Fig. 1c) was also investigated. Data about the water quality of brine discharge and its inflow rate was not available. Consequently, different percentages of variation in water quality (for instance 10%, 50% of the initial values in the lagoons, shown in Table 2) were assumed and discussed under the same brine discharge of 1 m 3 /s. For more clarification, 10% variation in water quality, for instance, means that the DO decreased by 10% from its initial value in the lagoons, while the nitrogen and phosphours increased by 10% from their initial values in the domain.
Also, the effect of different brine discharges with values ranging from 0.05 to 1 m 3 /s was investigated. Moreover, the effect of different weather conditions on the propagation of polluted water was conducted.
The influence of each studied scenario was investigated by calculating the relative percent difference (RPD), as shown in Eq. (14): Finally, precautions have been discussed for the preservation of the desired water quality in the studied lagoons aiming for better dealing with the surrounding industrial and economical revolution and the expected climate change in the future. In this regard, new scenarios have been simulated investigating the effect of changes in the hydraulics of the lagoons and different operation scenarios of the nearby desalination plant. For instance, the effect of increasing the real width of the three open boundaries with the Red Sea has been discussed. Moreover, the effect of increasing the water quality of the inflow water (14) %RPD = (difference between maximum and minimum values)∕(average value) from the Red Sea by changing the input DO value as a main water quality indicator was analyzed. Also, the injection rapidity of the same quantity of brine disposals has been discussed (i.e., the comparison between rapid inflow of 0.4 m 3 /s in 1 day and slower inflow of 0.1 m 3 /s in 4 days and their effect on the water quality in the lagoons) in a trial to reduce their negative effects and help decision-makers in the city of El Gouna. Also, recommendations were given for decision-makers with regard to brine injection in specific weather conditions by simulating the effect of brine injection on water quality considering three different weather conditions: tide only, mean wind only, and tide with mean wind.

Maximum growth rate and half-saturation constants
From Eqs.
(2) to (4), the algal growth rate (CP) is mainly affected by the maximum phytoplankton growth rate (C max ), algal sunlight (K r1 ), and the growth limited by the availability of either phosphate or the sum of nitrate and ammonium μ(lim(phosphate, nitrate)), which, in turn, is affected by either the half-saturation constant of phosphate or nitrate. The sensitivity of the lagoons was investigated considering different referenced values (indicated in Table 3) of the aforementioned parameters by computing percental difference (%) and neglecting the sun effect to concentrate on the effect of nitrogen and phosphours. Table 4 indicates the fluctuations in tracer values under different maximum growth rate values (C max ), while Table 5 demonstrates the water quality variables under different half-saturation constant values of phosphate (KP). Both the maximum phytoplankton growth rate and the phosphate half-saturation constant directly affect the algal growth rate, which in turn has a major effect on the overall water quality. For instance, as shown in Tables 4 and 5, the average PHY highly increased by 200% percental difference, while the average L and DO received minor changes with differences not more than 3.25%. Moreover, PO 4 , NH 4 , and NO 3 decreased owing to the increasing algal growth with percental differences of 61.52%, 51.84% for PO 4 , 9.85%, 7.59% for NH 4 and 13.14%, 11.26% for NO 3 affected by changes in the maximum phytoplankton growth rate and the phosphate half-saturation constant, respectively. POR and NOR, on the other hand, increased by rates equal to 43.92%, 35.43% and 44.82%, 35.93%, respectively.
Besides, the domain was also investigated under different values of nitrate half-saturation constant (KN) since the growth rate was limited by the availability of either phosphate or the sum of nitrate and ammonium. The analysis of the results indicated that the domain was not sensitive to changes in the nitrogen half-saturation constant.

Mineralization rates
From Eqs. (10) and (11), the mineralization rate from NOR to NO 3 at 20 °C (K 620 ) directly affects NOR and NH 4 , which, in turn, affects the DO concentrations and the NO 3 (Eqs. 9 and 13). Table 6 illustrates the sensitivity of the aforementioned water quality variables to different mineralization rates. It can be observed from Table 6 that the variation in K 620 values has relatively high effects on the average NOR and NH 4 and has a minor impact on the average NO 3 and no effect on DO. For instance, the average NH 4 increased from 3.77 μg/l to reach a value of 4.47 μg/l with 18.57% increasing rate owing to the increase of K 620 value from 0.0 to 0.075/day. Moreover, the average NOR decreased by approximately 20% percental difference. The indirect effect of the K 620 increase had a slighter outcome on NO 3 , which increased by 3.32% by increasing K 620 value. On the other hand, DO was not affected by changes in K 620 values.
On the other hand, the mineralization rate from POR to PO 3 at 20 °C (K 320 ) affected only the values of PO 4 , POR (Eqs. 7 and 8) as indicated in Table 7. For instance, the average POR decreased by approximately 12% owing to the increase in K 320 from 0.001 to 0.05, while the average PO 4 increased from 1.95 to 2.51 μg/l owing to the same increase in K 320 .

Nitrification rate
From Eqs. (9) and (11), the nitrification rate at 20 °C (K 520 ) directly affects the values of NO 3 and NH 4 . DO concentration is indirectly influenced by the nitrification rate owing to its effect on NH 4 , as shown in Eq. (13). Table 8 illustrates the effect of different nitrification rate conditions on NO 3 , NH 4 , and DO in the lagoons.
It can be observed from the indicated average values in Table 8 that NH 4 and NO 3 are highly sensitive to the variations of the nitrification rate (K 520 ). For instance, NH 4 reduced from 8.64 to 2.43 μg/l and NO 3 increased by approximately 45% owing to the variation in K 520 . On the other hand, the DO was slightly affected by the aforementioned nitrification rate increase.

Benthic demand
As indicated in Eq. (13), the benthic demand only negatively affects the DO in the water domain. TELEMAC water quality manual suggests values of benthic demand ranging from 0.007 to 7 gO 2 /m 2 /day depending on the wastes coming to the water domain. As El Gouna City is not highly polluted, the lagoons were investigated under values of benthic demand that do not exceed 1.5 gO 2 /m 2 /day. The average DO values of 7.57, 6.82, and 6.07 mg/l corresponded to benthic demand values of 0.1, 0.8, and 1.5 gO 2 /m 2 / day. This reflects the high negative consequences of high benthic demand on the DO, which is considered the most vital parameter of aquatic life.  Degradation rate of L at 20 °C As indicated in Eqs. 12 and 13, both L and DO are influenced by the degradation rate of L, which varies between 0.1 and 1.5/day. Table 9 illustrates the negative effect of the L degradation load on water quality variables. It can be observed that the degradation rate highly affected L as its average value dropped from 2.29 to 0.33 mg/l by more than 85% decrease percentage due to the increase of the degradation rate. Also, the DO decreased from 7.81 to 7.57 mg/l owing to the same variation of degradation rate.

Phytoplankton respiration rate
Finally, the lagoons were investigated under different values of phytoplankton respiration rates considering values of 0.01,0.05, and 0.2/day. Table 10 illustrates the sensitivity of the water quality in the lagoons to the variation in respiration rate. It can be observed that the respiration rate has a small effect on approximately all water quality variable with differences not more than 2.2% for all variables except PHY and PO 4 which were relatively highly affected by − 20% and 8.44% percental differences affected by increasing RP, respectively.

Sensitivity analysis conclusions
From the aforementioned sensitivity analysis of nine input water quality parameters, it can be concluded that the maximum growth rate (C max ), the half-saturation constant of phosphate (KP) and the nitrification rate at 20 °C (K 520 ) have the most obvious effect on most of the water quality variables. For instance, both the maximum growth rate (C max ) and the phosphate half-saturation constant (KP) are highly affecting PHY, NOR, PO 4 , and POR, while the nitrification rate at 20 °C (K 520 ) has obvious effect on both NO 3 and NH 4 . On the other hand, the degradation rate of L is highly affecting L, while DO is influenced mainly by the benthic demand. It can be concluded that the water quality in the lagoons may be highly sensitive to any change in input parameters.
Although we have no field measurements, we think we have reasonable values for the discussed parameters and gained an insight into the sensitivity of the lagoons for each simulated parameter. Therefore, the suggested reference values indicated in Table 1 were applied to conduct the following scenarios, in which the effect of different water temperatures, different weather conditions, and the effect of the pollution from the nearby desalination plant was conducted.

Temperature impacts
The average water temperature in El Gouna City is calculated to be approximately 25 °C with a minimum value of 20.6 °C in winter and a maximum value of 30 °C in summer (Abouelsaad et al., 2022a). Consequently, the domain water quality was investigated under the aforementioned water temperatures. Figure 2 illustrates the effect of different water temperatures on the water quality parameters and the eutrophication problem after 6 days of simulations.
It can be concluded from Fig. 2 that the changes in water temperature affects most of the water quality variables. For instance, the increase in water temperature decreased the average DO from 8.25 to 6.94 mg/l and PHY from 0.09 to 0.06 μg/l corresponding to percental decreases of approximately 16% and 33%, respectively. Also, NO 3 and PO 4 increased from 19.23 to 20.63 μg/l and 3.22 to 3.40 μg/l in summer, respectively, while high temperatures had smaller consequences on NOR and POR, with difference percentages of not more than 2.5%. On the other hand, the warmer water had positive effects on L and NH 4 , which decreased from 1.44 to 1.02 mg/l and 4.68 to 3.28 μg/l owing to the decrease in removal rates.

Tide wave
Tide as a natural phenomenon can possibly affect water quality characteristics by moving pollutants upstream during high tide and downstream at low tide. In this regard, the effect of the tidal wave with 0.6 m amplitude on the eight water quality variables affecting the lagoons was studied. Figure 3 indicates the temporal fluctuation of these water quality variables (i.e., PHY, DO, total amount of phosphate (TP), which equals the summation of POR and PO 4 , and total amount of nitrate (TN), which equals the summation of NO 3 , NH 4 and NOR). It indicates the difference in water quality at three observation points On the other hand, the effect of the tidal wave on the average water quality variables, except DO, was small. While points near boundaries showed a higher effect of tidal wave than the inner points of the lagoons, especially at points with high flow velocities' fluctuation (i.e., point 1073 showed higher effect followed by point 2600 and point 1914).

Wind speeds
The effect of different wind speeds ranging from 8.24 to 4.01 m/s with the same wind direction of the northwest, which was computed during the study period of approximately 2 years was separately investigated. Firstly, the tidal wave was neglected to spotlight the effect of changes in wind speeds. Figure 4 clarifies the relationship between different wind speeds and water quality variables (PHY, DO, TP, TN), and the corresponding correlation coefficients R 2 assuming linear regression. Further, water quality variables were simulated under the effect of the beforementioned different wind speeds considering the tide effect. Table 11 indicates the average difference percentage (RPD %) between the average water quality characteristics corresponding to the high wind speed (8.24 m/s) and the low wind speed (4.01 m/s) in the whole domain in both cases. Also, the lagoons were divided into three areas: upper area (area 1), bottomleft area (area 2), and bottom-right area (area 3) as shown in Fig. 1c. In this regard, the average difference in the most influenced area in the lagoons under the two cases of different mean wind neglecting and considering the tidal wave was also discussed. It can be seen from Fig. 4 and Table 11 that changes in wind speeds are highly affecting the water quality variables in the lagoons producing correlation coefficients R 2 ranging from 0.64 to 0.76. For instance, the average PHY and DO in the whole domain decreased by approximately 48% and 7%, respectively for decreasing wind speed. Nutrients such as PO 4 , POR, NO 3 , and NOR increased with decreasing of wind speeds by a rate ranging approximately from 7 to 13%. Area 2 was the most affected area by declining wind speeds with a reduction of 63% for PHY and 9% for DO.
Further, while considering the tidal wave, the effect of variations in wind speeds on different water quality variables decreased. For instance, the whole average PHY and DO decreased to approximately 23% and 4%, respectively influenced by decreasing wind speeds. Nutrients, on the other hand, showed increased values with smaller differences, when compared to the previous case with no tide wave. The bottom right part of the lagoons showed a relatively high influence with a difference of 27% for PHY and 4% for DO.

Wind speeds and wind directions
Water quality in the lagoons was discussed, herein, considering variations in both wind speeds and wind directions ignoring the tide effect. From metrological data in the study period (from 2015 to the end of 2017), the mean wind was 5.24 m/s from the northwest direction, while the maximum wind was 20.8 m/s from the southeast direction. Different wind directions can play a chief role in the distribution of water quality variables close to inflow and outflow boundaries. Figure 5 shows different water quality variables at the three observation points 2600, 1073, and 1914 close to inflow/outflow boundaries (indicated in Fig. 1c) and the average values in both beforementioned scenarios and the corresponding flow velocities.
It can be seen from Fig. 5 that the water quality variables in both scenarios displayed no ups and downs in their variations as occurred in the case of tide effect only. Also, the maximum wind showed a relatively higher quality of water when compared to mean wind regardless of the wind direction and flow direction. For instance, lower nutrients and higher PHY and DO were observed in the case of maximum wind, when compared to mean wind. Also, the water quality variables in the three observation points in both scenarios were affected by flow direction (inflow or outflow point) and flow velocity. For instance, in the case of mean wind only, inflow point 2600 had a relatively higher water quality with high average DO concentration and low nutrients when compared to the outflow points 1073 and 1914. On the other hand, in the case of maximum wind only, outflow point 2600 had approximately close water quality to the water quality beside inflow points 1073 and 1914 owing to high outflow velocity.

Comparison between different weather conditions
Finally, Figs. 6 and 7 focus on the spatial PHY and DO at the end of 6 days of simulation under the effect of the three detailed weather conditions: tide only, mean wind only from the northwest direction and maximum wind only from the southeast direction. It can be concluded that each weather condition has a high effect on the spatial and temporal water quality in the lagoons.

Sensitivity analysis of different initial values of brine tracers' concentrations and different inflow brine discharges
The effects of different initial values of brine tracers' concentrations and different inflow brine discharges were discussed due to the lack of field data about the brine's inflow. It is known that brine water has a relatively low water quality. Herein, water quality of brine effluent was expressed using different percental decreasing rates of water quality of the lagoons. For instance, a 10% decreasing rate means that the brine inflow has values of 90% for DO and 110% for nutrients and phosphorus from the initial values in the lagoons. The average water quality variables in the whole domain affected by the brine disposals and their corresponding values at observation point 845, which is located just beside the desalination boundary (Fig. 1c), are illustrated in Table 12. It is indicated from the table that the average water quality variables in the lagoons were not highly affected by different brine tracers' concentrations or different inflow brine discharges. For instance, the average PHY presented neglected changes. DO reduced to an average value of 7.16 mg/l when the brine water is highly polluted (50% decreasing rate) and inflow has a high rate (1 m 3 /s), when compared to an average DO concentration of 7.62 mg/l at low brine pollution (10% decreasing rate) with low inflow rate (0.05 m 3 /s).
On the other hand, point 845 was highly sensitive to changes in tracers' concentrations and brine inflow owing to its location near the desalination inflow. For instance, the difference in the degree of pollution in brine discharge (10% and 50% decreasing ratios of the initial water quality variables) decreased PHY from 0.22 to 0.16 μg/l and DO from 7.48 to 6.46 mg/l, while TN and TP increased from 6.85 to 7.28 μg/l and from 29.86 to 38.44 μg/l, respectively. Different inflow brine discharges did not show high effects in case of low water pollution (10% decreasing rate) and were small compared to inflow brines range from 0.05 to 0.2 m 3 /s. On the other hand, increasing the brine inflow rate with highly polluted water (50% decreasing rate) could highly decrease water quality beside the desalination plant. For instance, DO decreased from 6.46 to 4.95 mg/l owing to the increase of inflow brine from 0.1 to 1 m 3 /s.

Different weather conditions
Finally, the propagation of brine disposals in the lagoons was discussed under the effect of three weather conditions: tide only, mean wind only, and high wind only. The same inflow of 0.1 m 3 /s with tracers' concentration with a 20% decreasing rate was used for the three scenarios. Figure 8 displays the effect of brine disposals on DO as a main indicator of water quality in the lagoons and its propagation. The brine movement was significantly influenced by tide and wind conditions. It mainly concentrated beside the desalination boundary and spread upward with a low rate to leave the lagoons through the top boundary under the effect of the tidal wave, whilst it followed mainly the same direction of the mean wind to outflow through the left bottom boundary in the second scenario. Finally, the maximum wind direction once again drove the brine upwardly and helped it to leave the domain rapidly.

Precautions for preservation of water quality in the lagoons
The water quality in the lagoons has been investigated under the effect of different precautions or changes in the hydraulics and the operating system of the nearby desalination plant aiming for preservation of the water quality in the lagoons. From the simulations, new recommendations for the decision-makers are presented and can help in the preservation of the water quality in the lagoons. For instance, larger inflow boundaries help to increase DO from 7.48 to 7.76 mg/l, as shown in Table 13. Also, increasing the DO concentration of inflow water from 7 to 8 mg/l helps to increase the average DO concentration in the whole domain from 6.66 to 7.54 mg/l in only 4 days. Moreover, the operation of the desalination plant plays a vital role in the disposal propagation in the domain. Consequently, it is recommended to inject the brine in time of tide with mean wind and not in time of tide only to quickly get rid of disposals and seeking better water quality, as indicated in Table 13.

Discussion
This work presents a complete insight of the water quality of artificial lagoons in El Gouna City. To the authors' knowledge, no previous studies discussed the water quality problems in manmade lagoons. Moreover, the advanced TELEMAC-EUTRO-WAQTEL module was, for the first time, applied to investigate the water characteristics in the lagoons using more than 25 input parameters. In this regard, a sensitivity analysis of different input parameters in the newly applied module was firstly conducted. The eutrophication problem in the lagoons displayed high sensitivity to changes in many of the input parameters. For instance, both the maximum growth rate of phytoplankton (C max ) and the phosphate half-saturation constant (KP) highly affected PHY, PO 4 , NOR, and POR. Also, the nitrification rate at 20 °C (K 520 ) had an obvious effect on both NO 3 and NH 4 . L, and DO, on the other hand, depended mostly on the degradation load of L and benthic demand, respectively. Afterwards, the effect of different meteorological data such as water temperature, tide wave, and wind speed on different water quality parameters was investigated. In a globally warming climate, air temperature is expected to increase by 1.1-6.4 °C by 2100, which, in turn, rapidly increases water temperature (Anthony et al., 2009). Moreover, Langodan et al. (2017) revealed the future definite tendency toward lowering the strength of wind speed in the Red Sea. Additionally, this work sheds new light on the effect of different wind directions on the water characteristics. The results showed that the high water temperature showed a negative obvious effect on some of the water quality characteristics as the increase of water temperature decreased DO and increased nutrients pollutants such as NO 3 , NOR, and PO 4 . The obtained negative effects of water temperature on different water parameters concur with previous studies by McLusky and Elliott (2007) Trombetta et al. (2019). Moreover, for the tide effect scenario, the fluctuations of water depth in case of tide wave also created a wave of ups and downs in water quality of points near boundaries, especially DO. Concentrations of DO fluctuated with approximately 0.3 mgO 2 /l differences between ups and downs corresponding to 0.6 m amplitude of tide wave. The obtained results concur with previous study by Zhu et al. (2017), who found regular and periodic variations in DO concentrations following the tidal cycles in the study area. Also, other pollutants showed ups and downs fluctuations near the boundaries affected mostly by high fluctuation in flow velocities. On the other hand, the average values of the water pollutants showed minor fluctuations of ups and downs inside the lagoons and away from boundaries. The applied wind speed and direction had a high effect on the eutrophication problem in the lagoons. For instance, considering the effect of different wind speeds, decreasing wind speed from the same wind direction was negatively affecting water quality variables in the lagoons, especially on the bottom left side. The high negative effect of decreasing wind speeds decreased when tide wave was combined with the effect of the differences in wind speeds. The negative effect of the expected decrease in wind speeds on the water quality in the lagoons concurs with a previous study by Deng et al. (2018), who found that decreasing wind speed coincided with increased P in their studied shallow eutrophic lake. On the other hand, the wind direction also had a high impact on the spatial water quality variables at inflow and outflow boundaries. For instance, points beside inflow boundaries had relatively higher PHY and DO values and lower nutrients, when compared to outflow boundaries, especially at low wind speeds.
El Gouna lagoons receive binary discharge from a nearby desalination plant, which alter the water characteristics in the lagoons. To date, the effect of desalination effluents on water characteristics in coastal areas has not been comprehensively investigated yet, despite the research interest on desalinated water characteristics is raising. In this regard, this work focuses on the harmful effect of pollution from the nearby desalination plant on the eutrophication process in the lagoons considering different weather conditions and different pollution intensity of desalination's effluent. Sensitivity analysis of different discharges and pollutions from the nearby desalination plant showed that different initial tracer concentrations did not highly affect the average water quality in the lagoons: however, the area just beside the inlet of the binary discharge showed a high negative effect, especially in the case of a highly polluted brine with a large inflow rate. Moreover, the simulation showed that the propagation of the tracers from desalination outflow was strongly affected by the weather conditions, as they moved upward in case of tide wave and maximum wind scenario, while they moved downward in case of the mean wind.
Finally, this study serves as a steppingstone for further work toward new precautions or changes in the hydraulics and the operation system of nearby desalinations plant seeking better water quality. For instance, larger inflow boundaries and injecting tracer in time of tide and mean wind instead of in the time of tide only or mean wind only are new suggested precautions.

Conclusions
A two-dimensional vertically averaged water quality numerical model using the TELEMAC-EUTRO-WAQTEL module has been applied to investigate the eutrophication water pollution problem in artificial lagoons of El Gouna City, which are highly stressed by the increasing tourism activities. Eight water quality variables were discussed: PHY, DO, PO 4 , POR, NO 3 , NOR, NH 4 , and L. The lagoons were found highly sensitive to metrological parameters such as water temperature, tide cycles, and wind patterns. The negative effect of the upcoming climate changes of higher water temperature and low wind speeds on the water quality in the lagoons was discussed. Moreover, the lagoons were also investigated under the negative effect from the nearby desalination plant, which throws its binary discharge in the lagoons. Finally, new precautions in the hydraulics and the operation system of nearby desalinations plant were discussed. Such precautions and a reduction in the external nutrient loading are needed, and their importance will increase in a future warmer world to help the lagoons facing the future climate circumstances and the polluted effluent from desalination plant.
This investigation is regarded as a preliminary and crucial step toward gaining a comprehensive understanding of water quality in El Gouna artificial lagoons and their environmental preservation. Having a broader picture of the water quality in the lagoons is critical for initiating dialogs with stakeholders and decision-makers in the area, as well as embracing mitigation steps to safeguard El Gouna's ecosystem and the adjacent coral reefs.