# Decision-Making Challenges of Sustainable Groundwater Strategy under Multi-Event Pressure in Arid Environments: The Diyala River Basin in Iraq

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study Identification

^{2}. The land surface elevation ranges between 1809 and 88 m.a.s.l. The average annual rainfall and mean temperature (T

_{mean}) are 285 mm and 24 °C, respectively [29].

^{9}m

^{3}, with storage coefficients for the upper and lower aquifer estimated at 3.5% and 0.14%, respectively [31]. The central part of Diyala river basin has many cities, villages, and farms. Since the 1980s, about 1800 wells were drilled [29] in the area due to urban and rural development and associated regional water exploitation increase. Moreover, the government intends to develop and invest in six irrigation projects covering a total area of 647.4 × 10

^{6}m

^{2}[29,32]. The average aquifer pumping discharge (${Q}_{Av}$) within projects areas is about 778 m

^{3}/day, which is calculated using spatial analysis in ArcGIS 10.2 depending on the wells’ discharges available in the historical database [29] (Figure 2b).

^{6}m

^{3}[29,32]. This is set within the context of 30 years of meteorological data (precipitation and evapotranspiration) 1981–2010 presented in Table 1 [29]. The maximum field capacity, according to [33] in [31], is 115 mm, with the surface runoff being equal to 7% of the direct rainfall [34]. The expected future gross total agricultural economic benefit is 160 million USD per year. Hence, the decision makers will require robust water resource management strategies to enable economic benefits to be realized without jeopardizing the sustainability of the water resource.

#### 2.2. Identification of Groundwater Flow Model

_{xx}, K

_{yy}, and K

_{zz}are the hydraulic conductivities of the media in x, y, and z direction, respectively. W is a source or sink of water, S

_{s}is the specific storage of the aquifer, h and t represent the groundwater level and time, respectively. Harbaugh and McDonald (1996) present MODFLOW-96 package as a groundwater model solver for steady and unsteady flow. An updated version of MODFLOW-2005 was presented by Harbaugh [36].

_{t}) occurs due to the infiltration of access water precipitation (P

_{t}) or irrigation water (IR

_{t}), when soil moisture (SM

_{t}) and the crop evapotranspiration (ET

_{t}) requirements are fully satisfied. The general soil–water balance equation to calculate the infiltrating amount of water to groundwater in the time period t + 1 can be expressed as:

_{t}is the surface runoff at time t. Deep percolation occurs when the moisture content in soil exceeds the maximum field capacity (maxSM) of the soil, which is defined by Allen et al. [37] as “the amount of water that a well-drained soil should hold against gravitational forces”. Hence, the deep percolation, in case of $S{M}_{t+1}$ > maxSM, can be found as follows

_{Sec}, the aquifer permeability K is the aquifer hydraulic conductivity, and I is the hydraulic (groundwater) gradient where I = ∆h⁄∆l, with ∆h being the difference between the water table head at the recharge and discharge zones of the specified aquifer, and ∆l is the separation distance. These parameters can be calculated using MODFLOW-2005 and GIS techniques. A regional groundwater model had not previously been developed and, hence, a complete regional 3D MODFLOW-2005 model was built for recharge estimation, as in Figure 3. The initial boundary head levels and wells parameters were extracted from wells log database and maps available in SGI et al. [29]. The regional water balance in Table 1 shows scarcity in water recharges from the rainfall due to high evapotranspiration rates (ET

_{o}> P), hence zero recharge from rainfall was considered for the simulation model [38]. The simulation model achieved static flow for parameter calibration. The model consists of four layers’ the first two layers are Bai-Hassan and Mukdadiya formation since the two formations are composed of course sediments and are hydraulically connected. The last two layers represent the Injana aquifer system, which is composed of alternation of clay and sand beds. The average thickness of the two systems is 2000 m. The average calibrated K value is about 2.67 m/day and 0.01 m/day for the upper and lower aquifers (Figure 4), respectively, while the upper aquifer boundary recharge TR

_{0}is about 4.88 × 106 m

^{3}/month.

#### 2.3. Regional Management Model Identification

_{t}) to fulfil the project’s monthly water demands over the proposed operation period. Table 2 shows the adopted scenarios and operation periods of the model.

_{t}) and the total groundwater withdrawal (G

_{t}) at time t with respect to the project’s maximum demands (PD

_{max}) over the entire considered period (T), which can be expressed by the following formula:

_{max}is the design maximum wells’ number, and C is a penalty factor that includes all models violations, which can be formulated as [40,41]:

^{4}was selected to exploit all feasible solutions and avoid rendering infeasible solutions at the constraint threshold, especially those with small violation values.

_{t}) can be estimated as:

_{t}) with respect to maximum soil field capacity (maxSM) over the considered period of time (T), which can be expressed as:

_{st}) in the aquifers during the extracting process at time t can be expressed as:

_{aq}is the aquifer storage calculated from the water balance equation as:

_{t}is the total water recharges to the aquifers at time t.

_{t}) can be estimated as:

_{t}) is equal or less than the project’s maximum water demands, while the monthly number of operated wells (Nw

_{t}) should not exceed the maximum design number (Nw

_{max}). Also, the monthly soil moisture content (SM

_{t}) should be greater than 50% of the maximum soil moisture content (maxSM) to avoid reaching wilting point, in which the plant will die, nor the value of (maxSM) to avoid water deep percolation.

#### 2.4. MOEA Method Identification

**x**) = (f1(

**x**), …, fm(

**x**))

^{T}; subjected to:

**x**∈ Ω, Ω is the decision space and

**x**∈ Ω is a decision vector. F(

**x**) consists of m objective functions f

_{i}: Ω → R

^{m}, i = 1, …, m where R

^{m}is the objective space.

**u**= (u

_{1}, …, u

_{m})

^{T}is said to dominate another vector

**v**= (v

_{1}, …, v

_{m})

^{T}if u

_{i}≤ v

_{i}for i = 1, …, m and u ≠ v. This can be defined as

**u**≺

**v**. Also, a feasible solution

**x**∈ Ω is called a Pareto-optimal solution; if there is no alternative solution

**y**∈ Ω such that

**F(y)**≺

**F(x)**, then the Pareto-optimal set, PS, is the union of all Pareto-optimal solutions, and may be defined as: PS = {

**x**∈ Ω:∄

**y**∈ Ω,

**F(y)**≺

**F(x)**}. The Pareto-optimal front (PF) is the set comprising the Pareto-optimal solutions in the objective space in a multi-objective optimization problem and is expressed as: PF = {

**F(x)**|

**x**∈ PS}.

^{6}to 1.2 × 10

^{6}in both scenarios.

## 3. Result

#### 3.1. Performance Analysis

^{9}m

^{3}) was predicted after 40 years of water exploitation, hence the 50-year alternative (600 months) is not presented here.

#### 3.2. Groundwater Optimum Management

^{6}m

^{3}/month, and it ranged from 15 × 10

^{6}to 20 × 10

^{6}m

^{3}/month for the open furrows system.

## 4. Discussion

#### 4.1. Model Performance

#### 4.2. Groundwater Management Results

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Geological and average aquifers discharge maps of the study area. (

**a**) geological map (GEOSURV, 1993); (

**b**) average aquifers discharges map extracted from the historical wells logs dataset and ArcGIS spatial analysis (UTM coordinate system).

**Figure 3.**MODFLOW conceptual model development from 3D fence, 3D sold, 3D cell, and 3D boundary conditions models using groundwater modelling system (GMS) software.

**Figure 4.**Generated parameters from MODFLOW model implementation in comparison with the database parameters for the aquifer permeability in meters/day and groundwater level in meters (above sea level), respectively.

**Figure 5.**Optimum solution Pareto-front for both irrigation alternative scenarios using both algorithms. f

_{Del-GW}, f

_{WL}, and f

_{mining}refer to groundwater delivery, water losses, and mining objectives functions, respectively.

**Figure 6.**Number of wells and deficit in water demands achieved for both scenarios for discrete periods using optimization model. f

_{Del-GW}, f

_{WL}, and f

_{mining}refer to groundwater delivery, water losses, and mining objectives functions, respectively.

**Figure 7.**Final groundwater storage achieved by optimization model for open furrows and drip irrigation system over the adopted discrete periods.

**Figure 8.**Illustrates the sustainable groundwater management periods achieved for 50 years for both irrigation systems using ε-DSEA.

**Figure 9.**Operators’ selection probability comparison between both algorithms for four adopted operating periods under selected irrigation alternatives scenarios. Each x-axis represents number of function evaluation, and all y-axis are operator’s selection probability.

**Table 1.**Average monthly meteorological data (mm) 1981–2010 within the central part of Diayal river basin [29].

Month | Rainfall P | Surface Runoff RO | Reference Evapo-Transpiration ETo | Total Water Balance P-RO-ETo |
---|---|---|---|---|

October | 14 | 0.98 | 131 | −117.98 |

November | 37 | 2.59 | 67 | −32.59 |

December | 46 | 3.22 | 38 | 4.78 |

January | 61 | 4.27 | 36 | 20.73 |

February | 44 | 3.08 | 48 | −7.08 |

March | 41.5 | 2.905 | 84 | −45.41 |

April | 33 | 2.31 | 122 | −91.31 |

May | 8 | 0.56 | 183 | −175.56 |

June | 0.5 | 0.035 | 229 | −228.54 |

July | 0 | 0 | 253 | −253 |

August | 0 | 0 | 234 | −234 |

September | 0 | 0 | 176 | −176 |

Annual | 285 | 19.95 | 1600 | −1334.95 |

Methods of Irrigation | Operation Periods (Months) | ||||
---|---|---|---|---|---|

Open furrows irrigation (scenario-1) | 12 | 60 | 120 | 300 | 600 |

Drip irrigation (scenario-2) | 12 | 60 | 120 | 300 | 600 |

Parameter | Limitations |
---|---|

Pumping discharge (m^{3}/month × 10^{6}) | $0<{G}_{t}\le 74.27$ (open furrow) $0<{G}_{t}\le 56.79$ (Drip) |

Number of wells (per month) | $1\le N{w}_{t}\le 3183.0$ |

Soil moisture content (mm/month) | $57.5\le S{M}_{t}\le 115.0$ |

Parameters | Borg | ε-DSEA ^{1} | Parameters | Borg | ε-DSEA |
---|---|---|---|---|---|

Initial population size | 100 | 100 | SPX parents | 10 | 3 |

Tournament selection size | 2 | 2 | SPX offspring | 2 | 2 |

SBX crossover rate | 1.0 | 1.0 | SPX expansion rate λ | 3 | [2.5, 3.5] |

SBX distribution index η | 15.0 | [0, 100] | UNDX parents | 10 | 10 |

DE crossover rate CR | 0.1 | [0.1, 1.0] | UNDX offspring | 2 | 2 |

DE step size F | 0.5 | [0.5, 1.0] | UNDX σ_{ζ} | 0.5 | [0.4, 0.6] |

PCX parents | 10 | 10 | UNDX σ_{η} | 0.35/$\sqrt{L}$ | [0.1, 0.35]/$\sqrt{L}$ |

PCX offspring | 2 | 2 | UM mutation rate | 1/L | 1/L |

PCX σ_{η} | 0.1 | [0.1, 0.3] | PM mutation rate | 1/L | 1/L |

PCX σ_{ζ} | 0.1 | [0.1, 0.3] | PM distribution index η_{m} | 20 | 20 |

_{η}and σ

_{ζ}are standard deviation control the distribution of decision variables.

^{1}The initial values of dynamic parameters used in ε-DSEA are as shown for Borg MOEA.

**Table 5.**Median summary of the best achievement for both algorithms under two irrigation alternative scenarios. The superior results are in bold (smallest values for minimum and largest values for maximum).

Objective | Borg MOEA | ε-DSEA | ||||||
---|---|---|---|---|---|---|---|---|

12 ^{1} | 60 | 120 | 300 | 12 | 60 | 120 | 300 | |

Scenario-1 | ||||||||

Min. f_{Del-GW} | 0.005 | 0.916 | 2.952 | 10.183 | 0.006 | 1.057 | 2.490 | 7.988 |

Max. f_{Del-GW} | 1.192 | 5.362 | 7.599 | 15.988 | 1.244 | 6.248 | 9.371 | 18.922 |

Min. f_{WL} | 0.274 | 2.05 | 6.387 | 19.934 | 0.161 | 1.476 | 4.329 | 12.839 |

Max. f_{WL} | 7.547 | 11.606 | 18.121 | 34.877 | 7.426 | 10.758 | 18.420 | 37.521 |

Min. f_{mining} | 12.145 | 65.077 | 143.648 | 544.399 | 12.142 | 65.05 | 143.169 | 528.478 |

Max. f_{mining} | 12.257 | 67.656 | 153.438 | 649.679 | 12.256 | 67.973 | 158.254 | 765.451 |

Scenario-2 | ||||||||

Min. f_{Del-GW} | 0.002 | 0.348 | 0.889 | 3.241 | 0.003 | 0.436 | 0.729 | 2.453 |

Max. f_{Del-GW} | 0.528 | 3.668 | 3.997 | 6.837 | 0.531 | 3.159 | 4.040 | 8.063 |

Min. f_{WL} | 0.149 | 1.067 | 3.758 | 12.311 | 0.146 | 1.074 | 3.430 | 9.864 |

Max. f_{WL} | 2.066 | 4.481 | 8.079 | 16.522 | 2.149 | 4.006 | 8.053 | 17.027 |

Min. f_{mining} | 12.121 | 64.599 | 141.408 | 516.02 | 12.120 | 64.607 | 141.288 | 506.564 |

Max. f_{mining} | 12.200 | 66.233 | 148.191 | 571.196 | 12.200 | 66.730 | 149.655 | 601.931 |

^{1}Number of months.

**Table 6.**Summary of pumping discharges and aquifer recharges for the optimum solution achieved by each objective function over considered periods using open furrows and drip irrigation system (m

^{3}/month × 10

^{6}).

Operating Periods (Years) | ${\mathit{f}}_{\mathit{D}\mathit{e}\mathit{l}-\mathit{G}\mathit{W}}$ | ${\mathit{f}}_{\mathit{W}\mathit{L}}$ | ${\mathit{f}}_{\mathit{m}\mathit{i}\mathit{n}\mathit{i}\mathit{n}\mathit{g}}$ | ${\mathit{f}}_{\mathit{D}\mathit{e}\mathit{l}-\mathit{G}\mathit{W}}$ | ${\mathit{f}}_{\mathit{W}\mathit{L}}$ | ${\mathit{f}}_{\mathit{m}\mathit{i}\mathit{n}\mathit{i}\mathit{n}\mathit{g}}$ |
---|---|---|---|---|---|---|

Mean | Median | |||||

Pumping discharge—Scenario-1 | ||||||

One | 45.95 | 27.48 | 27.56 | 51.67 | 37.78 | 37.96 |

Five | 39.81 | 26.93 | 30.24 | 44.00 | 35.44 | 42.00 |

Ten | 38.97 | 29.75 | 31.94 | 43.51 | 36.87 | 41.15 |

Twenty-five | 37.43 | 31.44 | 33.06 | 42.22 | 35.99 | 41.32 |

groundwater recharge—Scenario-1 | ||||||

One | 18.31 | 3.34 | 3.99 | 16.46 | 0.00 | 0.00 |

Five | 18.20 | 5.42 | 11.62 | 8.08 | 0.00 | 2.11 |

Ten | 17.91 | 7.60 | 13.26 | 7.78 | 0.00 | 2.46 |

Twenty-five | 16.15 | 8.79 | 14.06 | 7.79 | 1.17 | 3.88 |

Pumping discharge—Scenario-2 | ||||||

One | 35.12 | 24.24 | 24.20 | 38.45 | 33.73 | 33.95 |

Five | 30.94 | 24.46 | 24.28 | 34.02 | 32.89 | 33.40 |

Ten | 31.49 | 25.56 | 27.39 | 33.88 | 30.79 | 33.46 |

Twenty-five | 30.61 | 27.11 | 27.26 | 33.63 | 32.23 | 33.24 |

groundwater recharge—Scenario-2 | ||||||

One | 11.63 | 3.14 | 3.32 | 6.80 | 0.00 | 0.00 |

Five | 11.36 | 4.21 | 6.79 | 5.02 | 0.00 | 0.00 |

Ten | 11.91 | 5.85 | 9.80 | 5.11 | 0.00 | 1.23 |

Twenty-five | 10.88 | 7.81 | 9.24 | 5.04 | 0.99 | 1.43 |

_{Del-GW}, f

_{WL}, and f

_{mining}refer to groundwater delivery, water losses, and mining objectives functions, respectively.

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**MDPI and ACS Style**

Al-Jawad, J.Y.; Al-Jawad, S.B.; Kalin, R.M. Decision-Making Challenges of Sustainable Groundwater Strategy under Multi-Event Pressure in Arid Environments: The Diyala River Basin in Iraq. *Water* **2019**, *11*, 2160.
https://doi.org/10.3390/w11102160

**AMA Style**

Al-Jawad JY, Al-Jawad SB, Kalin RM. Decision-Making Challenges of Sustainable Groundwater Strategy under Multi-Event Pressure in Arid Environments: The Diyala River Basin in Iraq. *Water*. 2019; 11(10):2160.
https://doi.org/10.3390/w11102160

**Chicago/Turabian Style**

Al-Jawad, Jafar Y., Sadik B. Al-Jawad, and Robert M. Kalin. 2019. "Decision-Making Challenges of Sustainable Groundwater Strategy under Multi-Event Pressure in Arid Environments: The Diyala River Basin in Iraq" *Water* 11, no. 10: 2160.
https://doi.org/10.3390/w11102160