Assessment of Groundwater Flow for the Western Side of Al-Kut City, Southern Iraq

Abstract


Introduction
Groundwater resources are the largest freshwater storage (Rahnama et al., 2013 ( Groundwater can be considered of the most important natural water resources worldwide because several small towns and big cities around the world rely on as a main source of water supply because of its inexpensive extraction quality, and abundance (Morris et al., 2003).In many environments, during periods of low or no rainfall natural groundwater discharges keep rivers, lakes, and wetlands flowing.Natural groundwater recharge takes place by both recharge from rain, and concentrated recharging by infiltration from overland waters (lakes, swamps and streams), and it relies significantly on the current climate, subsurface geology, and land cover.When compared to soil and geology, climate and land cover have a significant impact on precipitation and evapotranspiration (Taylor et al., 2013).The use of numerical modeling techniques in groundwater research is now commonplace.To assess the quantitative and qualitative effects of the existing situation and future development on source groundwater, simulation computer resources, a powerful instrument in the best exploitation of the source, are evaluated (Dehghani, 2013).Groundwater models are a scientific and predictive tool for assessing optimum water allocation, surface water-groundwater interaction, landscape management, and the impact of new development scenarios (Kumar, 2013).Simply, a model of groundwater is similar to a glass tank filled with moist soil, but in sophisticated way, it is similar to a 3D mathematical representation required thousands of formulas and equations to be calculated by a powerful computer, (U.S. ACE, 1999).Groundwater models use mathematical equations based on specific simplifying assumptions to represent groundwater flow and transport processes.Models of groundwater flow help manage groundwater resources because they provide an approximation of the different geological and hydrological characteristics.These models also used for providing an obvious representation of the flow pattern of the aquifer.groundwatermodeling studies have given researchers a greater knowledge of how aquifers function and how the demand for water for the home, agricultural, and industrial applications is continuously increasing.Therefore, it is essential to manage the groundwater resources in the best possible way.Management methods cannot be created until a more precise evaluation of the groundwater potential has been completed.It has been demonstrated that using mathematical models in conjunction with thorough field research could be useful for this.Actually, a model is approximation solving method rather than it is an exact representation for field circumstances due to the assumptions suggested in the depended mathematical formulas and various uncertainties in needed data.Even as approximations, groundwater models are a useful exploration tool that groundwater hydrologist can employ for a variety of applications.(Kumar, 2002).The fast development in the usage of digital computer models has improved groundwater management.For example, mathematical modeling was utilized in the simulation technique that is concerned with predicting natural groundwater under the impact of various stresses.The mathematical models are essentially a collection of equations subjected to particular assumptions, initial circumstances, and boundary conditions to describe the physical active processes in an aquifer.In general, a model can be used to depict a simplified version of reality if it is properly designed (Khalaf and Hasan, 2013).The mathematical models consist of partial differential equations.The general equations for simplified subset can solve by analytical models, and these describe the situations of idealized that are limited in the application.There are many studies in which the modflow program was used to model groundwater, Rejani et al. (2008) developed a two dimensional groundwater of flow and transport model of the Balasore basin in India by using Visual MODFLOW package of analysing an aquifer response for strategies of various pumping the results showed that a sensitivity analysis indicated that the system of Balasore aquifer is more susceptible for seepages of the river and recharges from interflow and rainfall than the vertical and horizontal hydraulic conductivities and the specific storage.Chakraborty et al. (2020) are used Visual-MODFLOW 2000 for analysing the groundwaterlevel simulation in Purba (East) Midnapur, West Bengal, India, the result concluded that the groundwater flow occurs from south to north direction of East Midnapur, as the saline water intrusion from the nearby sea takes place into the aquifers towards inland direction.Ansarifar et al. (2020) studied the impact of groundwater levels on structures and infrastructures of coastal areas in the Bandar-e-Gas coastal aquifer in the Gorgon Gulf region in northern Iran.They simulated groundwater levels by using the MODFLOW mathematical model.The mentioned results confirm the precision of the model for the entire simulation period; they also indicate that the simulation has a limited underestimation behavior.Moreover, it shows that the precision of the results has negligible variability, which means the simulation also has considerable reliability.

Location of the Study Area
The study area is located on the western side of Kut city in Wasit, Iraq.Between Tigris River and Al-Gharraf river, it extends to the administrative borders of Kut.It covers an area of about 122 km 2 Between 32° 30ʹ 0ʺ N to 32° 26ʹ 30ʺ N latitude and 45° 48ʹ 0ʺ E to 45° 52ʹ 0ʺE longitude, as shown in Fig. 1, Where shows the location of the observation wells are presented.Kut city is situated on Tigris River 180 km southeast of Baghdad city.The city center is a peninsula encircled by Tigris on three sides.Near its northern side there are two branches, one of them is Al-Gharaf and the other is Al-Dujaili.The area of the governorate is 17.153 km 2 .It has a semi-arid climate of hot dry summer, cold and wet winter.Water for the Wasit comes mostly from the Tigris River and, secondly , from the Al-Garraf branch, which receives its water from Tigris upstream of Kut Dam.In Iraq, Tigris runs from north toward south, many dams and hydraulic structures were constructed for controlling the water flow and for irrigation purposes (Mashaan et al , 2015).The study area is divided into two parts, a residential area, and an agricultural area, and it is considered fertile land because it is in the middle of Tigris River and its branches in the city of Kut.Its land is almost flat.Fig. 1 shows the study area and observation wells

Fieldwork
Based on premilmenry survey The wells distributed were determined according to their location with Tigris and Al-Gharraf rivers branching from the river.Five points were excavated at a depth of 8.5 meters and 6 inches in diameter with different distances between one point and another .4-inchdiameter tubes were dropped into the holes and the rest of the holes were filled with a graduated filter with a diameter of 5-19 mm.The points were identified to cover the area between Tigris River, and Al-Gharraf river.The location of the wells was determined in a way that ensures complete coverage of the study area The study area consists of a residential part and the other agricultural part, and its coordinates are shown in Table 1.The daily readings of the control wells were taken 24 hours after drilling, that is, after the stability of the groundwater levels.Daily readings were recorded for six months,and the average daily readings of Tigris and Al-Gharraf rivers were taken for the study period to know the extent of their impact on the movement of groundwater in the western side of the city of Kut.The hydraulic conductivity was calculated by taking soil samples at the sites of observation wells and calculating the conductivity value in the laboratory.

Data Collection
After completing the drilling of the wells and after stabilizing the water levels in them and reaching a stable state after 24 hours, the depth measurement was started from the level of the natural ground to the depth to groundwater level with the sounder.Daily monitoring for depth to groundwater levels in the wells were taken in observation wells that were drilled for a period of 6 months to monitor groundwater level For the months (January, February, March, April, May, June).The measurement of groundwater levels in the wells began on 26 December 2021 and continued until 30 June 2022.Data were collected for the levels to the downstream of Kut barraged, as well as the upstream for Al-Gharraf river and the downstream They were taken as points in Tigris River in the study area for the same period The average reading was taken and Enter them as fixed points of the ratio in the mathematical model.

The Mathematical Model
GMS, a US-developed computer program used as predictive tools to ascertain future conditions or the impact of a proposed action on the current subsurface groundwater system in order to create a mathematical model and make it easier to solve differential equations, established a network in the western part of Kut city.They can also be used in regulatory mode as general or screening techniques for generating management standards and guidelines.(Bedient et al., 1994).The total area of study is about 26.8 km2 with a circumference of approximately 23.2 km.The numerical model (modflow) has been prepared in the form of a grid, the number of columns is 70, the number of rows is 75, the total number of cells is 5250, the active cells are 2544, and the ineffective 2706 Fig. 2 shows the network of cells in the study area of the mathematical model.Some parameters have been entered into the mathematical model, such as hydraulic conductivity, recharge, available information for groundwater levels in the region where was the rate of hydraulic conductivity Equal 0.0135 cell thickness that is related to the upper and lower levels of the aquifer.The study area is an aquifer that is unconfined to a single layer.The thickness of the layer was taken at 30 meters, and the average was taken for the value of the hydraulic conductivity as it is close to values, obtained from laboratory testing of soil in control wells After determining the coordinate system of the area, the western side of Kut city, the model was prepared as a first step by incorporating a topographic image (WGS 1984 UTM zone 38 N).Then a conceptual model is prepared and given the appropriate name.The groundwater modeling system (GMS 10.0) was used to represent the model for the study area.

Boundary Conditions
Depending on the method of finite difference, the controlling equations related to the flow of groundwater flow can be solved.Basically, the solution needs for both initial and boundary conditions of the actual physical model, these conditions must be described exactly in the numerical model (Batu, 2005).
Mathematical boundary constraints must be used to represent hydrological features adjacent to and inside the model domain.In MODFLOW, there are three types of boundary condition simulation cells, the first ine is no-flow cells, the second is constant head cells and the third type variable-head cells .The first type provides specified head with time where the head value does not change according to the solution of flow equations.The second cells are those that do not allow any flow into or out of the cell.With the grid's leftover cells, dubbed "variable-head" cells.The mathematical model was modified in the study area, which considered the aquifer as non-confined.All nodes outside the limits of the simulation area were identified as fixed-head nodes (inactive cells) and the internal elements were applied as variable head elements.
The starting limits were taken in the stationary state, which is the distribution of the head within the model area at the start time (time zero) and then the head was adjusted in the aquifer in the study area so that the levels of the groundwater correspond to the level of pressure measurement.
The INBOUND matrix, which has a symbol for each cell in a model, was used to input the requirements for the study area boundaries.In MODFLOW, each cell's boundary-condition type is expressed as an integer array.
Where: The row and column numbers are i and j, respectively, and the layer number is K.
Fig. 2 shows the grid and boundary conditions of the study area model.

Model Parameters
To prepare the mathematical model, it needs the model operation parameters in the application of the steady and unsteady state representation, as shown in the following: • Hydraulic conductivity: It is considered an influential factor in the model of groundwater.It can be determined using the constant head permeability test.In the current area of study, the initial hydraulic conductivity values were evaluated using the wells, as shown in Table 2., and these records were applied as the starting values in the model The hydraulic conductivity of the model after calibration equals 0.0135.At this value, the results of the model were acceptable, • Hydraulic head at the start: When starting the program and making simulations for the movement of groundwater, it takes hydraulic heads for beginners at first to simulate the flow.To simulate the transient flow, the initial headers must be real values because they correspond to the calculation of storage items ,Initially to represent the steady-state flow, starting vertices were applied as initial values to solve the iterative equation.The starting vertices of fixed vertices are real while all other values can be applied to a random height many modeling objectives, such as analysis of average groundwater flow patterns and flow rates and an estimation of mean annual seepage from the lost stream, calculation of territorial waters, table gradients, and simulation of long-term pumpingaffected flow trends, have often been addressed with a steady-state solution alone.(Anderson et al, 2015) .The data was used for five wells that were drilled in the study area, where the average values were used to derive an initial fixed hydraulic head for the study area, as shown in Table 2. Fig. 3 shows the initial hydraulic head for the study area.• The recharge rate for the study area: Among the transactions that are entered in the preparation of the model for the study area is the amount of recharge in the area, where the estimated values they recharge were entered for the study area and were estimated according to information about rainwater and irrigation wate , As well as leaking from the rivers adjacent to the study area from the Public Water Resources Department.
• Top and bottom elevations of the simulated aquifer : Prepare a mathematical model in the MODFLOW program for the study area, which requires entering the hydrogeological properties of the aquifer for the study area Including a map showing the values of the bottom of the aquifer, the values of the surface of the aquifer, and the amount of the initial groundwater levels for the region (starting head), because the aquifer in the study area is of the type unconfined aquifer, so the top elevation is equal to the starting head in a steady-state.Table 2. shows the bottom and top elevation of the well points.Figs. 3 and 4 shows top and bottom elevation for the aquifer.

Calibration of the Model
It can be defined as the process of fine-tuning the structure and values of model parameters to get the best possible fit between measured and simulated data.
Hydraulic heads and flows are measured.The model was calibrated.Achieved in both the steady and transient simulation conditions of flow There are two types of calibration processes: the first is a trial-and-error procedure in which calibration parameters are manually altered over and over again.This method may be thought of as a crucial first step in history matching since it can provide the modeler with a lot of information about the site being modeled and how parameter changes affect different regions of the model and different sorts of data Anderson et al 2015 The second form is automated parameter estimation, which can often be used to quickly calibrate a model.PEST (Parameter Estimation) GMS 10.4 Tutorial: (MODFLO, 2018( is a GMS interface to the mentioned calibration.PEST calibration can be done in two ways: zonal and pilot point calibration. The first method (zonal) is the most often used and is used in this investigation.For the unconfined aquifer, the hydraulic conductivity value is applied as the starting condition for the calibration process After entering the data, the model is run in a steady state, and the resulting head values are checked with the starting head values.In any mathematical model, the more convergence we get between the calculated values from the program with the starting head values (which represent groundwater levels in reality), the more accurate the results of the model After entering the data, the model is run in a steadystate, and the resulting head values are checked with the starting head values.

Model Sensitivity Analysis
Analysis of sensitivity is the process of changing the input parameters of the model to a reasonable extent and observing the associated change in the model's response.Usually, changes are noticeable in water discharge and head.Generally, the main aim of sensitivity analysis is for showing the models sensitivity for simulating the inexactitude in the input data values of the model.Further more, analysis of sensitivity is important to determine the trend of future activities of data collection, when the used model becomes sensitive to certain data, this implies that the data requires future description, unlike the data when the model exhibits relative insensitivity.The sensitivity analysis of the model was performed automatically in the PEST method The hydraulic conductivity and recharge coefficients were modified to the negative values for the modflow software to understand that the model would undergo a sensitivity analysis.The hydraulic conductivity value was changed to -10 and they recharge value was changed to -30 were given for re-feeding The program starts by changing the coefficients until it reaches values that give a small error rate ,The head values are close to the values that were calculated in the study area .the model is more sensitive to the recharge.

Model Validation
People who use groundwater models and those who rely choices on model results naturally want reassurance that the model is reliable (Popper, 1959).Groundwater models specifically have been subjected to the same idea (Oreskes et al., 1994).
The standards for designating a model as validated are by their very nature arbitrary.By comparing computations with field or laboratory measurements, validation is performed using the same method that is more appropriately and generally referred to as calibration.But even with a poor or inaccurate model, a reasonable comparison can be made because model solutions are not all unique.
There is some disagreement about validation because of semantics.In hydrology, the word validation and verification are frequently used interchangeably.Although some define validation as a method of demonstrating the ability of a site-specific method model to depict causal links in a given domain region and validation as a means of demonstrating efficiency in the governing equation using a general model, one of the stated goals of validation is to increase confidence in the model's ability to produce reliable predictions .
In this case, the model was verified by running it at the flood level of the Tigris and Gharraf rivers , The flood level of Tigris River is 18.40 meters and theAl-Gharraf River is 18.20 meters.

Results and Discussion
The results of calibrating the model showed a closeness between the values obtained in the model and the average values calculated in the control wells, where the average of the lowest value of the measured head in the region was equals to 17.9 and the highest value was equals to 18.88 and the values of the head of the model ranged between 15.2-18.8Fig. 5 shows the results of the head values when the model is calibrated , shows that the calibration stage led to a good improvement in the distribution of factors, and it concludes that the model successfully represents the steady-state, as a close coincidence was obtained between the records and representative heads.Fig. 6 shows the comparison between the results obtained from the model after calibration with the data that were calculated from the study area

Conclusions
Developing a mathematical model for finite variance requires a wide range of hydrogeological and hydrological data for aquifers.The mathematical model is an effective management tool for aquifer studies and prediction of the various impacts of hydrological and hydrogeological tensions.Such a purpose is closer to reality when modeling and calibration stages successfully.The conceptual model was built using the geological and hydrogeological conditions collected along with the digital elevation model (DEM) data.Hydraulic conductivity was applied to 5 wells in the study area.A groundwater flow model was developed in the steady state for the western side of Kut city.The groundwater source for the study area comes from the surface water represented by the Tigris River.The model was calibrated and the results of the head distribution were similar to those measured in the study area.A sensitivity analysis was performed and it was found that the model is sensitive to recharge.A groundwater assessment database has been established for the western side of the city of Kut, which provides researchers in the future with a picture of the groundwater in the region and the extent of the possibility to benefit from this natural resource.

Fig. 2 .
Fig. 2. Grid and boundary conditions of study area model

Fig. 5 .
Fig.5.Head distribution in the study area in the mathematical model

Fig. 6 .Fig. 7 .
Fig. 6.The comparison between the results obtained from the model after calibration with the data that were calculated from the study area

Fig. 8 .
Fig.8.The distribution of the head at the flood level of Tigris andAl-Gharraf rivers

Table 1 .
Coordinates of well drilling points for the area between the Tigris River and the Gharraf River

Table 2 .
Hydraulic factors related to the observation wells in a steady region