ABSTRACT

Lake Edku is one of the northern Nile Delta lakes in Egypt. It suffers from a high level of eutrophication. Lake Edku suffers from pollution from a variety of sources, including municipal and agricultural waste. This study presents a simulated model for a hydrology system that provides a challenge in predicting hydraulic residence time or how water contaminants circulate over the time. Hydraulic residence time is realized as a measure of how rapidly water quality will be affected by changes in pollutant loadings. A hydrological model was created to predict the hydraulic residence time for Edku Lake using a modular three-dimensional finite-difference groundwater flow model called “MODFLOW”. The model revealed that the accurate hydraulic residence time for Lake Edku is 14, 25, 20, and 10 days for autumn, winter, spring, and summer correspondingly, with a 17.25-day yearly average. However, this study presents many challenges in understanding how hydraulic residence time is determined by considering the interaction between surface water and subsurface water. Lake hydraulic residence time calculations are considered a useful water quality management tool in preparing the proceedings and solution scenarios that in turn will contribute to lake restoration efforts.

1 INTRODUCTION

The main issue with lakes is that their annual water budget is influenced by a wide variety of water resources. Estimating hydraulic residence time in lakes using various models will provide innovative insight that could clarify numerous other metrics related to lake water quality. It can also be utilized to clarify whether lakes are more or less vulnerable to watershed disturbances that lead to lake impairment. Nutrient, pollutant, and other chemical concentrations in lakes are directly impacted by hydraulic residence time. Hydraulic residence time can also be a guide to predicting the risk of accelerated eutrophication in lakes. Estimates of residency times will be provided by this study. The Lake Hydraulic Residence Time is considered a hydrologic management guidance for sustainable development, especially for lakes. Additionally, it will allow enhanced lake models and a better comprehension of how pollution cycles take place.

Usually, apparent inputs and outputs are used to estimate lake hydraulic residence time; groundwater exchange is typically not taken into account. This study presents many challenges in clarifying how hydraulic residence time varies depending on surface water and subsurface water resources inputs and outputs, such as evaporation rate, precipitation, streams, and groundwater contributions (inflow and outflow).

Previously, this approach was used as a tool for defining water source exchange; however, in this study, it was used for predicting hydraulic residence time for lakes. Thus, this study has allowed researchers to determine hydraulic residence time with extremely high accuracy without long data sets. Lake residence time will be driven by taking into account lake morphology, stage fluctuations, evaporation rates, precipitation, groundwater fluxes, and flow into and out of a lake. The accurate estimation of these fluxes and their interaction with the water body directly correlates to the accurate prediction of residence time. Therefore, these fluxes are quantified and modeled to give an accurate estimated hydraulic residence time for a specific lake. A few previous studies reported results about estimating hydraulic residence times depending on many factors and ignoring others.

For conservative chemicals, the hydraulic residence times in the Great Lakes vary considerably, ranging from slightly over two years for Lake Erie to approximately 200 years for Lake Superior (Quinn 1992).

Rueda (2001) reports on several fairly recent studies that use numerical 3D modeling to determine renewal time. Among the seven bays taken into consideration in his research, he analyzes the measurements and experiments carried out on Little Sodus Bay. In the numerical experiments, a tracer (of mass m_o, represented in kg) was measured at a specific location, and its progression over time (t) was simulated. The following equation was used to get the mean residence time (τ_γ):

(1)

Five months of simulations were conducted using an accurate system for lake hydrodynamic phenomena that accounts for turbulent and chaotic flow. This system, in particular, permits the use of Navier-Stokes equations and incorporates a Mellor-Yamada scheme for turbulent systems (Rueda 2001; Rueda et al. 2003).

Essentially, these early methods highlighted the phenomenon's complications and indicated the necessity for more precise data on lake hydrodynamics, which is also a crucial requirement for figuring out the actual residence time for water in each basin. Also, Weiss et al. (1991) confirm that one of the needs for realization of how a lake ecosystem functions chemically, biologically, and physically is its rate of deep water renewal by interaction with surface waters. This interaction controls the local distribution of water properties controlling the time-dependent response of the lake to its functions.

Ambrosetti et al. (2003) analyze and take into account the agents that participate in these procedures and provide a more practical definition for hydraulic water residence time that considers these agents and their effects on internal hydrodynamics. These agents, such as consequent thermal stratification, evaluate the stabilizing effects of the surface layers, the wind force, and the water flowing into the lake from the tributaries, while also taking account of the local and regional climatic situation.

Quinn (1992) determines the residence time for the Laurentian Great Lakes, North America. In his study, groundwater exchange and lake evaporation were not considered in the residence time calculation.

For Lake Edku, Badr and Hussein (2010) determined residence time for each season by dividing the lake volume by the seasonally varying lake outflow rate. Their study ignores the subsurface water interaction between groundwater and lake water. Their results are 26.41, 54.14, 33.23, and 20.69 days for autumn, winter, spring, and summer, correspondingly, with a 33.61-day yearly average.

Lake Hydraulic Residence Time calculations are considered a useful management tool for the restoration of lakes (Abd-El-Baky 2022).

2 STUDY AREA

Lake Edku is a brackish and shallow coastal basin with small islands that form sheltered ponds at its western edge. It is located 30 kilometers to the southeast of the Nile Delta. Alexandria is located on the eastern shore of the lake. It is situated between latitude 30°10' to 31°18'N and longitude 30°8'30" to 30°23'E (Figure 1).

Figure 1 Location map of Edku Lake, Egypt.

Lake Edku is one of Egypt's most endangered aquatic wetlands, and it is the third largest coastal lake in the northern Nile Delta. Abd-El-Baky (2025) presented location, importance, threat, action plan, and general strategies of Egyptian wetlands. Human activities and other man-made pollutants seriously influence it. Geographically, the Lake Edku basin is bordered by fish farms, agricultural land, and urban areas [Behaira Governorate]. A large amount of fishing and agricultural waste is dumped into the lake by the adjacent drains, especially the Barsik and El-Khairy drains. As a consequence of these numerous surrounding activities, several problems affect its ecosystem.

Lake Edku is connected to Alexandria, to Rosetta about 19 000 m to the northeast via a railway and a coastal road, and approximately 42 000 m to the west southwest. From the beginning of the 20th century to the present, Edku Lake has been subjected to many sources of pollution. The various land use/cover activities in the study area are depicted in Figure 2. Edku Lake is one of the most crtical lakes to anthropogenic activities. As seen in Figure 2, Edku Lake is situated at the south of Abu-Qir Bay. In order to exchange and circulate water between the lake and the sea, it is connected to the Mediterranean Sea.

Figure 2 Land use and drains for Edku Lake (Said et al. 2022).

2.1 Aquifer medium

The groundwater flow system via the aquifer is impacted by the aquifer medium. The Quaternary sediments, which mostly comprise Nile silt, clay, sandy clay, sands, and gravels completely enclose the Nile Delta region (Elewa and El Nahry 2008).

2.2 Biodiversity of the ecosystem in Lake Edku

The wetland agricultural areas include sedge meadows, floating and submerged reed swamps, and halophytic features. Typha domingensis grows abundantly in the reed swamp habitat that is typically dominated by Phragmites australis. The floating type is dominated by Eichhornia crassipes, which is related to Jussiaea repens, Spirodela polyrrhiza, Azolla nilotica, L. gibba, Alternanthera sessilis, Wolfia hyalin, and Lemna minor. Ceratophyllum demersum, which is associated with Ruppia maritima, P. crispus, P. pectinatus, and Najas armata, dominates submerged agriculture. According to Birks et al. (2001), Juncus acutus, which is linked to Scirpus litoralis and Cyperus articulatus, as well as a few halophytes, such as Arthrocnemum macrostachyuns, Inula crithomides, Atribplex portulacoides, Salicornia fruticosa, and Zygophyllum album, dominate the sedge-meadow landscape. Numerous bacteria, including pathogenic coliforms which could endanger public health, aquatic life, and animals, and could also be introduced by sewage (Siam and Ghobrial 2000) .

2.3 Edku Lake’s population, economics, and drainage system

Edku Lake is situated in Markaz Edku, which has a population of 6,670,630 people, according to the 2021 statistics issued by the Central Agency for Public Mobilization and Statistics (CAPMAS). Most lakes suffer from a variety of issues related to population growth, such as industrialization, urbanization, and agricultural development, all of which have an effect on the environment of the lakes (Abd El-Hamid et al. 2021) .

As stated by Badr and Hussein (2010), there are several sources of contamination in Edku Lake, including the following: large amounts of drainage waters are released into the lake by the Barsik and El-Khairy drains; El-Bousely, Edku, and Damanhour sub-drains are three sources of drainage waters that El-Khairy Drain is connected to. These sub-drains carry wastewater from houses, agricultural lands, and industries; they also carry the drainage water from over 300 aquaculture farms. Barsik Drain mostly supplies the lake with agricultural drainage water, and Boughaz El-Maadia at Abu Kir Bay, a shallow basin, provides seawater to the lake's northwest. This drain receives a significant amount of raw industrial waste from numerous factories via El-Tabia Pumping Station (on average, 2 · 10⁶ (m³/day)) (Moneer et al. 2023). The majority of people are employed in agriculture, fishery, and industrial activities (Abd El-Hamid et al. 2021).

Three ill-defined basins can be distinguished inside the lake: the eastern, middle, and western. Edku, Bersik, El-Khairy, and El Bousily are the four main drains that open into the lake's eastern basin and provide the lake with an enormous amount of drainage water (Okbah and El-Gohary 2002). The discharge of agricultural and industrial wastewater in Edku Lake Basin has led to a significant contamination issue, particularly with certain heavy metals like Cadmium metal (El‐Amier et al. 2018). The primary issue causing Edku Lake’s distortion is human encroachment (Sheta et al. 2022). When wastewater is dumped into natural water bodies without being properly treated, organic matter grows and oxygen levels drop (Gupta et al. 2014). Agricultural and industrial wastewater cause contamination of surface-water basins by adding excess nutrients and some chemicals.

The Kom Belag Drain releases roughly one-sixth of the wastewater from the Bersik Drain (Shetaia et al. 2020). The annual drainage water discharged from the El-Khairy Drain is 592 × 10⁶ (m³) and the Bersik Drain is 348 · 10⁶ (m³) (Zakaria and El‐Naggar 2019; Moneer et al. 2023).

The influx of seawater through Boughaz El-Maadia takes place as the result of the action of the wind. This connection maintains the lake stage at approximately the same as the sea level. However, if the sea level at high tide and low tide affects the fluxes, in this case, it is very important to include a tide action as a boundary condition in the model, especially in the small timesteps. However, it is assumed that there are two water currents at the lake-sea connection, where subsurface water from the bay enters the lake and surface water flows from the lake to Abu-Qir Bay in the opposite direction (Shakweer 2006; Moneer et al. 2023). Most of the time, this drainage water provides water that flows through the lake from the west, and from the south to the north, towards the sea (El Kafrawy and Ahmed 2020).

3 METHODOLOGY

Estimating hydraulic residence time in lakes using numerical hydrological models provides innovative solutions that could illustrate several other measurements related to quality issues of lake water and provides more accurate results in the hydraulic residence time predictions.

In the past, the hydraulic residence time predictions have been represented by using the water balance equation, and then considering the outflow rate from the basin through its outlet. Moreover, the evaporation rate and groundwater in/out flow are ignored. Additionally, the hydraulic residence time is typically determined by dividing the lake's volume by its outflow rate. Furthermore, most hydrological models have represented either surface water or groundwater alone. It is attributed to the complex interaction between surface water and groundwater.

For instance, surface models like PRMS, HBV, or SWAT were employed to simulate the interactions between groundwater and surface runoff. Conversely, other models, such as AQUIFEM-1 and MODFLOW, simplified surface processes while focusing on the groundwater component (El Zehairy 2014). As a result, current research endeavors to attempt to improve hydrological models and their applications to become integrated models by considering the interactions between surface and groundwater.

This study not only uses the integrated hydrological model but also uses it for hydraulic residence time predictions. Surface-groundwater interactions required the dynamic integration of lake and groundwater fluxes by using MODFLOW-6 with some specified packages, including the Evapotranspiration Package (EVT), Stream Flow Routing Package (SFR), Lake Package (LAK), and Recharge Package (RCH).

3.1 MODFLOW-6 Overview

MODFLOW-6 is a program developed to support a platform for providing numerous models in the same simulation. Typically, it is called ‘‘MODFLOW’’ (MODular three-dimensional finite difference ground water FLOW model). The reason this version of MODFLOW includes a "6" is because it is the sixth core version that the US Geological Survey (USGS) has produced; the other core versions were available in 1984, 1988, 1996, 2000, and 2005. This current version of MODFLOW-6 is version 6.4.4, released February 13, 2024, and can be downloaded via MODFLOW-6: USGS Modular Hydrologic Model | U.S. Geological Survey. 

The graphical user interface software environment, ModelMuse, facilitates the creation of MODFLOW input files (Winston 2009). The model's temporal and spatial data are derived from the stress periods and the grid, respectively. The model stress periods, data sets, grids, objects, formulas, and model features are all part of the fundamental design needed to use ModelMuse.

A simulation may incorporate any number of models in the new design. By adding these models to the same numerical solution, they can be made to be closely associated at the matrix level, or they can be made to be not dependent on one another and not interact, or they are able to exchange information. Model development and usage are made possible by the isolated information transfer across models to exchange items. A regional-scale groundwater model and several local-scale groundwater models may be connected to this new version. Alternatively, several groundwater flow models could be connected to a surface water flow model. Future extensions of the framework, such as the simulation of solute transport, are automatically supported. Recently, Langevin et al. (2022) used MODFLOW to simulate the Groundwater Transport Model by using the three-dimensional transport of a single solute species in flowing groundwater. MODFLOW was first developed by McDonald and Harbaugh (1988). They used Equation 2 to describe the three dimensions of incompressible groundwater flow through porous media.

(2)

Where:

Kx, Ky, and Kz	=	hydraulic conductivity values in the coordinate axes (x, y, and z) (L/T);
t	=	time (T),
h	=	potential head (L),
Ss	=	“specific storage” of material’s porous (L-1), and
Wv	=	a volumetric discharge / unit volume representing sources and/or sinks of water, with W = -ve for groundwater system outflow, and W = +ve for groundwater system inflow into the system (T-1).

3.2 Conductance coefficients equation

The groundwater storage terms and the CR, CV, and CC conductance coefficients are computed by the internal flow packages in MODFLOW and used in the flow equation, which is expressed as finite difference flow equation No. 2.26 in the document “MODFLOW-2005” (Harbaugh 2005) (Equation 3).

(3)

Where:

i,j,k	=	(i) indicator for the column, (j) indicator row, and (k) indicator layer directions, respectively,
CVi,j,k-1/2	=	intercell conductance between cells i,j,k-1 and i,j,k,
CRi,j-1/2k	=	intercell conductance between cells i,j-1,k and i,j,k,
CCi-1/2,j,k	=	intercell conductance between cells i-1,j,k and i,j,k,
CVi,j,k+1/2	=	intercell conductance between cells i,j,k and i,j,k+1,
CRi,j+1/2,k	=	intercell conductance between cells i,j,k and i,j+1,k,
CCi+1/2,j,k	=	intercell conductance between cells i,j,k and i+1,j,k, and
HCOFi,j,k	=	head‑coefficient term (collects all coefficients, multiplying the unknown heads that don’t include conductance between nodes).

All the right hand side terms of previous equation were integrated into the term RHS_i,j,k as well as the boundary conditions and the terms of storage (Harbaugh 2005).

The fact that the dry cells are not set in no flow conditions as they are in the HUF, LPF, or BCF Packages distinguishes the UPW Package from the the other three packages. If arithmetic averaging is applied in this case, it is inconsistent with flow continuity for water to outflow from a dry cell to a nearby partially saturated cell, which might lead to model convergence failure. Upstream weighting is used by the "UPW Package" to stop flow out of a dry cell and to maintain hydraulic conductance equals zero between a dry cell and a neighboring wet cell. As a result, a dry cell can be kept active by the UPW Package while preventing water from flowing out. When harmonic averaging is used during the rewetting of cells, similar problems appear. For all unconfined aquifer situations, upstream weighting provides a continuous solution. If there is a deeper layer, inflow to a dry cell from overlying cells, neighboring cells, or an external source represented using one of the stress packages naturally flows downward to a lower cell (Niswonger et al. 2011).

This presumption ignores the quantity of water that remains in the cell and assumes that the vertical conductance is constant. The groundwater flow equation states that horizontal conductance equal zero in a dry cell (i.e., the head is below the bottom of the cell) that is underlain by a partially or fully saturated cell. Using the flow into the dry cell, the head of the dry cell is computed using Equations 4a–c, below:

(4a)

(4b)

(4c)

Where:

Qi,j,k+1/2	=	volumetric flux rate between nodes i,j,k and i,j,k+1,
	=	sum of influx to the cell i,j,k from nearby cell or an external source,
hi,j,k	=	dry cell’s head, and
CVi,j,k+1/2	=	conductance coefficients between node i,j,k and i,j,k +1.

Hydraulic residence time (day) was typically calculated, in most previous studies, manually by dividing water volume (m³) by outflow rate (m³/day). The lake's entire volume of water losses and gains were measured or estimated in order to evaluate the water budget balance for the lake. Additionally, throughout the same time period, the corresponding change in the lake water water volume is measured. Estimating all the components of the water budget is a major challenge in surface water lake management. Because aquatic ecosystems are essential to human life, there is a rapid increase in the number of investigations into the water budget. One of the hardest aspects of the water balance to assess is the discharge of groundwater into or out of a lake. Lake systems may also be constrained by extremely low hydraulic gradients, which can be challenging to quantify precisely.

However, the present work addressed some fundamental issues related to the structure and functions of lakes, especially environmentally threatened lakes. This study takes into account:

1. Change in lake volume, which is related to continuous lake surface area changes, which are related to the fluctuation in lake stage according to the change of fluxes in/out of the lake over time.
2. All inflow/outflow water fluxes, either surface or subsurface water, at the beginning of model operation, then setting inflow water from drains to zero to investigate how long the lake would take to drain through its outlet.
3. Amount of inflow water as subsurface water from groundwater to the lake only.
4. Precipitation is the inflow of water to the lake during the winter season only.
5. Outflow water as a subsurface leakage from lake to groundwater.
6. Evaporation as outflow water from the lake during the summer season only.
7. Recharge water was estimated as excess irrigation water from surrounding agricultural lands.
8. Evapotranspiration water was estimated from surrounding agricultural lands. 

4 RESULTS AND DISCUSSION

4.1 Hydrological input parameter

For the hydrological input data, the recharge rate and hydraulic conductivity were extracted from the maps in Armanuos et al. (2020), which represent the recharge rate (mm/year) and hydraulic conductivity (m/day) of the Western Nile Delta aquifer. With an average daily amount of 0.05 million (m³), direct precipitation on Lake Edku's surface is mostly limited to the winter months. Restricted to the summer months, the average daily of evaporation rates from the lake was estimated to be 0.002 million (m³/d) (Badr and Hussein 2010). The drain El-Khairy and Barzik deliver the agricultural drainage water into Lake Edku. Table 1 lists the volumes of drainage water that were released from the drains. By using the water current meter, at Boughaz El-Maadia, direct measurements were made to determine the seasonal volume of the water outfluxes of Lake Edku (m³/d) to the sea (Badr and Hussein 2010), as shown in Table 2.

Table 1 Annual discharge (million m³) of agricultural drainage water into Lake Edku via drain El-Khairy and Barzik (Zakaria and El‐Naggar 2019).

Seasons	Drain Discharge
	El-Khairy	Barzik
Autumn	150	105
Winter	85	54
Spring	129	56
Summer	228	133
TOTAL = 940

Table 2 Outflow water from Lake Edku to the sea (Badr and Hussein 2010).

Seasons	Outflow million m3/day
Autumn	2.816
Winter	4.096
Spring	2.047
Summer	1.571

The ability of the aquifer's layers to transfer water, regulate groundwater flow, and convey contaminants is defined as hydraulic conductivity. The Western Nile Delta aquifer has a hydraulic conductivity ranging from 30 to 100 m/day (Armanuos et al. 2020). For topography in the area of study, the ground elevations ranged from 2.5 m above sea level to -5.47 m below sea level, with an average of 2.10 m below sea level. Figure 3 shows the ground levels presented as input data by the MODFLOW application.

Figure 3 Topographic map for the study area form the presented model using the MODFLOW application.

Water Balance

The basic hydrological equation, which states that the rates of influxes of water t from all resources minus the rates of outfluxes water equals the change in water storage volume in the study region over time, is typically used to assess a lake's water balance. It can be used to express the water balance for Lake Edku:

(5)

Where:

S	=	storage (m3/day),
V	=	volume (m3),
T	=	time (days),
Qin	=	total water inflow (m3/day),
Qout	=	total water outflow (m3/day),
P	=	precipitation (m/day),
G	=	groundwater flow (in or out) (m3/day),
As	=	lake surface area (m2), and
E	=	evaporation (m/day).

The lake's water surface area was 16.8 km², or roughly 4000 feddan (Hassan et al. 2023). The mean depth is 1.0 m and the maximum depth is 2.7 m (Badr and Hussein 2010). In the present study, the water surface area is approximately 15.75 × 10⁶ (m²), the maximum water volume is approximately 34.64 × 10⁶ (m³), and the maximum depth is 2.67 m.

4.2 Hydrological model results

Model results are displayed as a graph and analyses show how accurately the predictive model determines the hydraulic residence time of Edku Lake for each season. The hydraulic residence time is represented as the time the lake would take to drain its entire water volume through its outlet, considering all hydrology processes such as the groundwater interactions, precipitation, evaporation, evapotranspiration, and recharge of surrounding land. Also, the topography and features of aquifer media and other boundary conditions were adopted through the model. Additionally, the inflow water from drains is set equal to zero for model input data. Consequently, the presented model records drop in the lake stage every time step (one day). Therefore, there are daily changes in surface water area and water volume recorded by the model while it is running. Figure 4 gives the relation between daily stage, lake’s volume, and the water surface area of lake. The model reveals that the accurate hydraulic residence time is 14, 25, 20, and 10 days for autumn, winter, spring, and summer correspondingly, with a 17.25-day yearly average (see Figures 4 a, b, c, d).

Figure 4 Daily changes in surface water area and water volume for each season.

The cumulative hydrologic groundwater fluxes summaries for the simulated lake are sums of volumes added to the lake from the initial time until it drains the whole of its water volume through its outlet for each season. From the model result, there is an effective interaction between groundwater and lake water. Table 3 shows that the cumulative inflow water from groundwater to the lake was 6.92E+04, 9.60E+04, 9.85E+04, and 5.14E+04 (m³) for autumn, winter, spring, and summer correspondingly. The cumulative outflow water from the lake to the groundwater was 2.70E+04, 1.49E+04, 2.31E+04, and 3.85E+04 (m³) for autumn, winter, spring, and summer respectively. Therefore, cumulative net ground-water flow (inflow minus outflow) are 4.22E+04, 8.11E+04, 7.54E+04, and 1.29E+04 (m³). It can be noted from Table 3 that the higher amount of groundwater contribution is during the winter season. Consequently, it has an extreme effect on hydraulic residence time.

Table 3 Cumulative groundwater fluxes are sums of volumes gained/lost of the lake from initial time until it drains the whole water volume through its outlet.

Seasons	Inflow (from GW to Lake) (m3)	Outflow (from Lake to GW) (m3)	Net flow (m3)	Hydraulic residence time (day)
Autumn	6.92E+04	2.70E+04	4.22E+04	14
Winter	9.60E+04	1.49E+04	8.11E+04	25
Spring	9.85E+04	2.31E+04	7.54E+04	20
Summer	5.14E+04	3.85E+04	1.29E+04	10

The model utilized hydraulic residence time to estimate how long contaminants can reside in the lake basin. In most cases, hydraulic residence time is only evaluated by applying the lake’s volume and outflow rates. These methods don’t present the accurate values of existing hydraulic residence time. It is a critical and judgmental factor to consider cumulative groundwater fluxes gained/lost of the lake while preparing the procedures for hydraulic residence time predictions (see Figure 5).

Figure 5 Cumulative groundwater fluxes are sums of volumes gained/lost of the lake from the initial time until it drains the whole of its water volume through its outlet for each season.

For Lake Edku, Badr and Hussein (2010) determined residence time for each season. Their results were 26.41, 54.14, 33.23, and 20.69 days for autumn, winter, spring, and summer, correspondingly, with a 33.61-day yearly average. The model revealed that the accurate hydraulic residence time for Lake Edku is 14, 25, 20, and 10 days for autumn, winter, spring, and summer, correspondingly, with a 17.25-day yearly average. This is because the presented model does not ignore the subsurface water interaction between groundwater and lake water.

5 CONCLUSION

Lake Edku is suffering from huge inputs of pollutants and anthropogenic activity from surrounding agricultural lands, and sewage discharge draining into the lake. These conditions affect the lake's biological productivity. A major effort should be effective in controlling the eutrophication of Lake Edku, which has been directed toward reducing the input of contaminants.

• Lake Hydraulic Residence Time calculations are considered a useful water quality management tool in preparing the proceedings and solution scenarios that in turn will contribute to lake restoration efforts.
• The change in fluxes shows that the lake has an overall loss and gain in water from one season to another. Accordingly, Lake Hydraulic Residence Time changes from one season to another.
• Lake Hydraulic Residence Time in any aquatic ecosystem is a good indicator of the structure and function of the water ecosystem for lakes.
• Hydraulic pathways and lake water budgets, especially the groundwater fluxes in /out of the lake, are complex and variable in most lakes. Therefore, this study is considered one of the main engines of sustaining lakes in changing environments and pollution control issues. Accordingly, the present hydrological model has been developed to be an integrated model by taking into account the fluctuations in the lake stage according to the change of fluxes in /out of the lake over time. Therefore, this study is more accurate than previous studies.
• When using modeled hydraulic residence time, it is important to clarify seasonal and annual changes in the regional resources of the water basin and their catchment potential for contributing pollutants.
• By recording how the lake interacts over time with yearly fluctuations, agencies and stockholders are able to gain a better understanding of how to conserve, develop, and sustain lakes and their catchments.
• Hydraulic residence time is extremely important to provide a perspective on the impact of potential changes in contaminant loadings on the lakes.
• This study presents an integrated hydrological modeling program with general detailed steps to make it easy to apply to other case studies and handle many aspects of the application problem.
• Typically, the hydraulic residence time of lakes is calculated based only on apparent inflow and outflow; usually with exception of the exchange of groundwater. However, this study provides a challenge in comprehending how residence time is determined by considering the interaction between surface water and subsurface water.
• This model is characterized by its simplicity and few requirements.
• The MODFLOW-6 application is easy to use through ModelMuse (the graphical user interface) software environment which helps create input files for a MODFLOW-6 model. Additionally, it is developed periodically and available for free download from the USGS website.
• The results of this study will act as a warning for decision makers to take necessary actions and implement policies to reduce the environmental risk and maintain the healthy environment of the lake.
• The research's methodology, case study, and outcomes will help government agencies in managing, protecting, and developing the ecosystems and natural regional resources not only in Edku Lake, but also in other lakes that have the same features and environmental conditions. It is attributed to future plans according to the sustainable development strategy: ''Egypt Vision 2030''.

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