# Comparing Q-Tree with Nested Grids for Simulating Managed River Recharge of Groundwater

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{9}m

^{3}water was replenished to rivers and lakes in the Beijing-Tianjin-Hebei region by the south-to-north water diversion, as well as water diversion from the Yellow and Luan Rivers [5]. Thus, managed aquifer recharge by river has become a highly active field in the North China Plain.

## 2. Two Unstructured Grid Refinement Methods

#### 2.1. Q-Tree

#### 2.2. Nested Grids

## 3. A Simplified Model

#### 3.1. Model Setup

^{3}/d for each well.

^{5}m

^{3}/d, and the recharge period was set to 1 year.

#### 3.2. Four Grid Generation Schemes

#### 3.3. Simulation Scenarios

## 4. Results and Discussion

#### 4.1. Computational Efficiency

#### 4.2. Comparison of Simulated Flow Fields

#### 4.3. Simulated Relative Rise of Groundwater Level

#### 4.3.1. Comparison of Different Schemes

^{2}, while the corresponding numbers given by the Q-tree and nested models are 0.68 km

^{2}and 0.66 km

^{2}, respectively, both of which are quite close to the value given by the base model. By comparison, the corresponding area for the coarse grid model is only 0.33 km

^{2}, which is 55% smaller than that for the base model. Thus, the results show that the two unstructured grid schemes have higher simulation precisions and can characterize the morphology of contour lines in more detail than the coarse grid model.

#### 4.3.2. Effect of Boundary Conditions on Simulation Errors

#### 4.3.3. Effect of Refinement Degree on Simulation Error

#### 4.4. Differences in Groundwater Flow

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Fei, Y.H.; Cui, G.B. Development and Problems: Research on Artificial Adjustment of Groundwater Storage. J. China Hydrol.
**2006**, 26, 10–14. [Google Scholar] - Jonoski, A.; Zhou, Y.X.; Nonner, J.; Meijer, S. Model-aided design and optimization of artificial recharge-pumping systems. Int. Assoc. Sci. Hydrol. Bull.
**1997**, 42, 937–953. [Google Scholar] [CrossRef] - Jarraya Horriche, F.; Benabdallah, S. Assessing Aquifer Water Level and Salinity for a Managed Artificial Recharge Site Using Reclaimed Water. Water
**2020**, 12, 341. [Google Scholar] [CrossRef] [Green Version] - Dillon, P.; Fernández Escalante, E.; Megdal, S.B.; Massmann, G. Managed Aquifer Recharge for Water Resilience. Water
**2020**, 12, 1846. [Google Scholar] [CrossRef] - Chen, F.; Ding, Y.Y.; Li, Y.Y.; Li, W.; Tang, S.N.; Yu, L.L.; Liu, Y.Z.; Yang, Y.; Li, J.; Zhang, Y. Practice and Thinking of Groundwater Overdraft Restoration in North Plain China. South-to-North Water Transf. Water Sci. Technol.
**2020**, 18, 191–198. [Google Scholar] - Gupta, S.K.; Cole, C.R.; Pinder, G.F. A Finite-Element Three-Dimensional Groundwater (FE3DGW) Model for a Multiaquifer System. Water Resour. Res.
**1984**, 20, 553–563. [Google Scholar] [CrossRef] - Guo, W.X. Transient groundwater flow between reservoirs and water-table aquifers. J. Hydrol.
**1997**, 195, 370–384. [Google Scholar] [CrossRef] - Hao, Q.C.; Shao, J.L.; Hua, X.Z.; Zhang, X.G. A Study of the artificial adjustment of groundwater storage of the Yongding River alluvial fan in Beijing. Hydrogeol. Eng. Geol.
**2012**, 39, 12–18. [Google Scholar] - Niswonger, R.G.; Morway, E.D.; Triana, E.; Huntington, J.L. Managed aquifer recharge through off-season irrigation in agricultural regions. Water Resour. Res.
**2017**, 53, 6970–6992. [Google Scholar] [CrossRef] - Hao, Q.C.; Shao, J.L.; Cui, Y.L.; Zhang, Q.L.; Huang, L.X. Optimization of groundwater artificial recharge systems using a genetic algorithm: A case study in Beijing, China. Hydrogeol. J.
**2018**, 26, 1749–1761. [Google Scholar] [CrossRef] - Yao, Y.Y.; Zheng, C.M.; Liu, J.; Cao, G.L.; Xiao, H.L.; Li, H.T.; Li, W.P. Conceptual and numerical models for groundwater flow in an arid inland river basin. Hydrol. Process.
**2015**, 29, 1480–1492. [Google Scholar] [CrossRef] - Panday, S.; Langevin, C.D.; Niswonger, R.G.; Ibaraki, M.; Hughes, J.D. U.S. Geological Survey, MODFLOW–USG Version 1: An Unstructured Grid Version of MODFLOW for Simulating Groundwater Flow and Tightly Coupled Processes Using a Control Volume Finite-Difference Formulation; U.S. Geological Survey: Washington, DC, USA, 2013; p. 5.
- Krcmar, D.; Sracek, O. MODFLOW-USG: The New Possibilities in Mine Hydrogeology Modelling (or What is Not Written in the Manuals). Mine Water Environ.
**2014**, 33, 376–383. [Google Scholar] [CrossRef] - Naser, S.; Masoud, M.N.; Javad, F. A 3D unstructured triangular numerical algorithm for simultaneous effects of fluid density variation and water table gradient in saturated porous media. J. Hydrol.
**2019**, 568, 479–491. [Google Scholar] - Kumar, C.P. An overview of commonly used groundwater modelling software. Int. J. Adv. Res. Sci. Eng. Technol.
**2019**, 6, 7854–7865. [Google Scholar] - Samet, H. The Quadtree and Related Hierarchical Data Structures. ACM Comput. Surv.
**1984**, 16, 187–260. [Google Scholar] [CrossRef] [Green Version] - Yerry, M.A. A Modified Quadtree Approach To Finite Element Mesh Generation. IEEE Comput. Graph.
**1983**, 3, 39–46. [Google Scholar] [CrossRef] - Rogers, B.; Fujihara, M.; Borthwick, A.G.L. Adaptive Q-tree Godunov-type scheme for shallow water equations. Int. J. Numer. Meth. Fl.
**2015**, 35, 247–280. [Google Scholar] [CrossRef] - Liu, X.D.; Hua, Z.L.; Zhao, Y.P. Quad-Tree Meshes Based Godunov-Type 2-D Flow Numerical Model. J. Hohai Univ. (Nat. Sci.)
**2002**, 30, 6–10. [Google Scholar] - Đorđije, B.; Dušan, P.; Dragoljub, B.; Jelena, R. Hydrodynamic analysis of radial collector well ageing at Belgrade well field. J. Hydrol.
**2020**, 582, 124463. [Google Scholar] - Mehl, S.W.; Hill, M.C. MODFLOW–LGR—Documentation of Ghost Node Local Grid Refinement (LGR2) for Multiple Areas and the Boundary Flow and Head (BFH2) Package; 6-A44; U.S. Geological Survey: Reston, VA, USA, 2013; p. 54.
- Khan, M.R.; Koneshloo, M.; Knappett, P.S.; Ahmed, K.M.; Bostick, B.C.; Mailloux, B.J.; Mozumder, R.H.; Zahid, A.; Harvey, C.F.; Van Geen, A. Megacity pumping and preferential flow threaten groundwater quality. Nat. Commun.
**2016**, 7, 1–8. [Google Scholar] [CrossRef] - Forghani, A.; Peralta, R.C. Transport modeling and multivariate adaptive regression splines for evaluating performance of ASR systems in freshwater aquifers. J. Hydrol.
**2017**, 553, 540–548. [Google Scholar] [CrossRef] - Asher, M.J.; Croke, B.F.W.; Jakeman, A.J.; Peeters, L.J.M. A review of surrogate models and their application to groundwater modeling. Water Resour. Res.
**2015**, 51, 5957–5973. [Google Scholar] [CrossRef]

**Figure 5.**Comparison of simulated groundwater level (

**a**): 1 month; (

**b**): 6 months; and (

**c**): 12 months, unit of number at the contour lines is m.

**Figure 11.**Simulation errors in relative rise of groundwater level under different boundary conditions (

**a**): Dirichlet; (

**b**): Neumann; and (

**c**): General.

Grid Type | Number of Cells | Computation Time (s) |
---|---|---|

Coarse Grids | 1200 | 32 |

Q-tree Grids (3-degree refinement) | 2586 | 65 |

Nested Grids (local 125 m) | 3135 | 77 |

Q-tree Grids (6-degree refinement) | 15,771 | 362 |

Nested Grids (local 15.625 m) | 133,167 | 2347 |

Fine Grids | 1,228,800 | 18,126 |

Period | Grid Generation Scheme | Simulation Error (m) |
---|---|---|

1 Month | Coarse Grid | 0.29 |

Nested Grid | 0.10 | |

Q-tree Grid | 0.07 | |

6 Months | Coarse Grid | 0.37 |

Nested Grid | 0.22 | |

Q-tree Grid | 0.16 | |

12 Months | Coarse Grid | 0.38 |

Nested Grid | 0.24 | |

Q-tree Grid | 0.17 |

Schemes | Flow Volume (10^{4} m^{3}/d) | Error (Percentage) |
---|---|---|

Fine Grids | 16.8 | / |

Q-tree Grids | 16.2 | −3.6% |

Nested Grids | 16.1 | −4.2% |

Coarse Grids | 14.3 | −14.9% |

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**MDPI and ACS Style**

Cui, W.; Hao, Q.
Comparing Q-Tree with Nested Grids for Simulating Managed River Recharge of Groundwater. *Water* **2020**, *12*, 3516.
https://doi.org/10.3390/w12123516

**AMA Style**

Cui W, Hao Q.
Comparing Q-Tree with Nested Grids for Simulating Managed River Recharge of Groundwater. *Water*. 2020; 12(12):3516.
https://doi.org/10.3390/w12123516

**Chicago/Turabian Style**

Cui, Weizhe, and Qichen Hao.
2020. "Comparing Q-Tree with Nested Grids for Simulating Managed River Recharge of Groundwater" *Water* 12, no. 12: 3516.
https://doi.org/10.3390/w12123516