# Application of a Linked Hydrodynamic–Groundwater Model for Accurate Groundwater Simulation in Floodplain Areas: A Case Study of Irtysh River, China

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

## 2. Site Description

^{2}. The Piedmont plain in this basin is characterized by low precipitation levels, averaging less than 200 mm/year, and high evaporation rates, exceeding 1200 mm/year, making it a typical arid region. The focus of this paper is the floodplain area located in the middle reaches of the Irtysh River within the piedmont plain. The floodplain area has a width ranging from 10 to 12 km. The elevation of the floodplain area gradually decreases from east to west along the river, while it remains relatively constant along the perpendicular direction to the river. The elevation is approximately 600 m in the east and around 460 m in the west. Based on the temperature data obtained from the Burqin and Aletai hydrometric station, the study area exhibits a yearly average temperature of 4.7 °C, with a mean July temperature of 22.6 °C. The location of the Irtysh River basin is depicted in Figure 1.

## 3. Method

#### 3.1. Hydrodynamic Model

#### 3.1.1. Description of TELEMAC-2D Model

#### 3.1.2. The Establishment of Hydrodynamic Model

^{2}, consisting of 580,000 triangular grid cells and over 290,000 nodes. The terrain file is generated by assigning measured elevation point data, DEM data, measured elevation data of channel sections, and remote sensing data to each grid cell. The model includes four boundary conditions, including two inflow boundaries and two outflow boundaries. Figure 2 illustrates the simulation area, grid cell division, and boundary conditions of 2D hydrodynamic model.

#### 3.2. GW Model

#### 3.2.1. Description of MODFLOW Model

#### 3.2.2. The Establishment of GW Model

- (1)
- The simulation range and model boundary conditions should be determined. In this study, the focus is on the floodplain area in the middle reaches of the Irtysh River, covering approximately 1104 km
^{2}. The lateral boundary conditions, which consider terrain, geology, and flow field data, encompass inflow boundaries, outflow boundaries, and zero flow (or water separation) boundaries, as shown in Figure 3a. Reasons for this determination are as follows: The BC section and the EF section are considered as lateral inflow sections of GW, and thus generalized as inflow boundaries. The ED section, perpendicular to the GW contour, is treated as an impermeable boundary due to the absence of water exchange. The CD section, with the presence of a mountain named the Small Bashaan Mountain on the eastern side, creating a distinct flow field, is treated as an impermeable boundary. The FG section is influenced by topography and the southern irrigation area, making it a lateral inflow boundary. The south of the HG section is a desert area, and the terrain is relatively flat, resulting in minimal water exchange, and therefore HG is generalized as a zero-flow boundary. The AH section is where GW exits, and is hence generalized as an outflow boundary. Finally, the AB section, influenced by the northern irrigation area, is treated as a lateral inflow boundary. The vertical boundary conditions consist of ground at the top and an impervious layer at the bottom. - (2)
- The GW aquifer and source and sink terms should be correctly generalized. Based on the available hydrogeological data, the study area’s aquifers are characterized as homogeneous, isotropic single-layer unconfined aquifer. Considering the specific conditions, the GW model incorporates various recharge components, including floodplain flood GW recharge (FFGR), river channel seepage, canal system seepage, field irrigation infiltration, and lateral recharge. The method of obtaining FFGR will be discussed in the next section. River channel seepage is automatically calculated using the RIV package. Canal system seepage and field irrigation infiltration are calculated based on irrigation and canal data. Lateral recharge is computed using Darcy’s law formula, where hydraulic gradients are derived from GW contours. The main discharge components are represented by evapotranspiration, river channel discharge, and lateral GW discharge. Evaporation data are calculated by multiplying the evaporation coefficient (it has a value of 0.85 in this study) with the large water surface evaporation data from the meteorological station, and river channel discharge and lateral GW discharge are obtained using the same methods described above.
- (3)
- The model should be discretized in time and space.

- (4)
- The parameters should be determined.

#### 3.3. Hydrodynamic–GW Model Coupling Strategy

#### 3.3.1. Temporal Coupling

- (1)
- Generalization of the formula for FFGR:

_{0}, t

_{1}are the start time and end time of flood infiltration respectively. All the values of the above variables are greater than 0.

- (2)
- Extraction of hydrodynamic model results:

- (3)
- Determination of FFGR:

^{3}.

#### 3.3.2. Spatial Coupling

- (1)
- Analog range partitioning of hydrodynamic model:

_{1}, …, A

_{20}. Next, the number of zones for model partitioning is determined, along with the respective area of each zone. In this study, based on the hydrodynamic model simulation results in 2016, the simulation area of the hydrodynamic model is divided into three zones, and the area of the corresponding zones are S

_{1}, S

_{2}, S

_{3}. The division process is elaborated using Figure 5, where m, Ss, S

_{f}are intermediate variables.

_{1}as an example, a brief explanation of Figure 5 is provided. Assuming that there are two potential values for S

_{1}, A

_{1}and A

_{1}+ A

_{2}, if A

_{1}+ A

_{2}is only up to 5% larger than A

_{1}, which can be expressed as A

_{1}+ A

_{2}< 1.05 A

_{1}, then S

_{1}equals A

_{1}. Conversely, if the increase exceeds 5%, then S

_{1}= A

_{1}+ A

_{2}. By employing the aforementioned approach, the two-dimensional hydrodynamic model area is partitioned into three zones based on the proportion of inundation duration within the intervals of 0% to 5%, 5% to 80%, and 80% to 100% of the total duration. These three delineated regions have respective areas of 385 km

^{2}, 266 km

^{2}, and 388 km

^{2}, as illustrated in Figure 6.

- (2)
- Determination of FFGR in each zone:

_{n}is the average number of days submerged in the n-th zone; p represents the proportion of submerged days in the n-th zone to the total number of days; H, L are the lower limit and upper limit of p in the n-th zone, respectively; ${S}_{n}\left(p\right)$ is the area where the proportion of submerged days to the total number of days in the n-th zone is p; q

_{n}is the ratio of the average submerged days of the n-th zone to the total submerged days of the entire region, ${q}_{n}=\left({\sum}_{p=L}^{p=H}{S}_{n}\left(p\right)\u2022p\right)/{S}_{n}$. In this study, the values of q

_{1}, q

_{2}, q

_{3}are 2%, 50%, and 95%, respectively.

_{1}, W

_{2}, W

_{3}are the FFGR in zone1, zone2, and zone 3, respectively.

- (3)
- Correspondence of spatial location information:

## 4. Results

#### 4.1. Calibration and Validation of the Models

#### 4.1.1. The 2D Hydrodynamic Model

#### 4.1.2. The Coupled Hydrodynamic–GW Model

#### 4.2. Water Balance of the Coupled SW–GW Model

^{3}. Notably, the recharge from floodplain floods surpasses 300 billion m

^{3}in both 2016 and 2017. This substantial volume of water cannot be overlooked in GW numerical simulations. Additionally, “evaporation” constitutes the predominant portion of GW discharge. This can be attributed to the study area’s location in an arid inland region with high evaporation rates. Moreover, the discharge exceeds the recharge in both 2016 and 2017, indicating a rise in GW levels towards the end of the year. However, it is important to note that this discrepancy may be attributed to the accuracy of the GW model. In reality, the GW level should remain relatively stable throughout the year. Furthermore, the contribution of GW recharge from rivers and lateral boundaries is limited in the study area.

## 5. Discussion

#### 5.1. Accurate Spatiotemporal Simulation of GW Table

#### 5.2. Recommendations during Coupled Model Modeling

- Digital Elevation Models (DEMs) are vital for both hydrodynamic and GW modeling, and it is crucial to carefully check and correct them to ensure accurate simulation results. The hydrodynamic model’s accuracy is directly influenced by precise elevation data, as it determines flow rates and directions. Similarly, the GW model relies on accurate elevation information to assess the deviation between the model’s top elevation and the phreatic level, known as the phreatic depth. To enhance simulation accuracy, it is recommended to utilize measured elevation data for both hydrodynamic and GW models.
- Accurate zoning of the hydrodynamic model is crucial for the successful coupling strategy. In this study, the simulation range of the hydrodynamic model is divided into three zones based on the proportion of inundation time. The rationale behind this choice stems from the observation that finer partitioning based on the proportion of inundation time does not yield substantial differences in the resulting zone areas. However, pursuing a more refined partitioning approach would entail a significant increase in workload without commensurate benefits, rendering it cost ineffective. Therefore, it is recommended to determine the SW zoning based on the specific characteristics of the model.

#### 5.3. Model Limitations

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of the study area, including hydrometric stations, reservoirs, water management projects, and flow monitoring sites.

**Figure 3.**(

**a**) Lateral boundary conditions of GW model (A–H are the start and end points of each boundary); (

**b**) simulation area, parameter partition of GW model.

**Figure 4.**The coupling strategy of hydrodynamic model and GW model (1–11 are the order of each step of the coupling strategy).

**Figure 8.**Calculated (red) and observed (blue) hydrographs at Burqin, Sarbulak, and Halagou Mudao Bridge in 2016, 2017.

Data Type | Data Content | Effect | Source |
---|---|---|---|

Geological data | Channel section, 2.5 m contour line, measured elevation points with a precision of 1 km | Generating the simulation area and terrain file | Geological survey results of the study area |

DEM data with a resolution of 15 m | Generating the simulation area and terrain file | Bigemap | |

Hydrological data | 2 h outflow processes of the 635 and KZJE reservoirs | Inflow boundary | Reservoir operation and scheduling data |

Daily flows of Yinejihai engineering | Outflow boundary | Operation and scheduling data of Yinejihai engineering | |

Daily water flows of the Burqin Hydrological Station | Calibration and validation | Burqin hydrometric station | |

Daily water levels of the Burqin Hydrological Station | Outflow boundary | Burqin hydrometric station | |

Daily water flows of Sarbulak, and Halagou Mudao Bridge | Calibration and validation | On-site monitoring data | |

Meteorological data | Daily evaporation | Water loss calculation | Aletai hydrometric station |

Infiltration observation data | Water loss calculation | Field data | |

Remote sensing image data | Remote sensing imaging from the SPOT-6 satellite and Environment-1 satellite | Generating the simulation area and terrain file | Bigemap |

Data Type | Data Content | Effect | Source |
---|---|---|---|

Topographic geological data | Elevation data obtained from surveyed points with an accuracy of 1 km, Hydrogeological cross-section, soil properties, contour map of GW level | Model establishment | Geological survey results of the study area |

The DEM data with a resolution of 15 m | Model establishment | Bigemap | |

Recharge and discharge items | Daily evaporation | Model establishment | Burqin and Aletai hydrometric station |

Irrigation area and monthly amount of irrigation | Model establishment | Regional agricultural statistics annual report | |

Other | Measured data of GW level on the 10th, 20th, and 30th day of each month | Model calibration and validation | Field measurement data |

Observation Well | 7-zk1 | 7-zk2 | 7-zk3 | 7-zk4 | 10-zk1 | 10-zk2 | 10-zk3 | 10-zk4 | Mean Value |
---|---|---|---|---|---|---|---|---|---|

2016 | 0.79 | 0.63 | 0.25 | 0.18 | 0.05 | 0.88 | 0.55 | 0.74 | 0.51 |

2017 | 1.74 | 0.56 | 0.2 | 0.27 | 0.49 | 0.94 | 0.75 | 1.24 | 0.77 |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Jiang, Y.; Zhang, S.; Wang, D.; Chen, H.
Application of a Linked Hydrodynamic–Groundwater Model for Accurate Groundwater Simulation in Floodplain Areas: A Case Study of Irtysh River, China. *Water* **2023**, *15*, 3059.
https://doi.org/10.3390/w15173059

**AMA Style**

Liu Y, Jiang Y, Zhang S, Wang D, Chen H.
Application of a Linked Hydrodynamic–Groundwater Model for Accurate Groundwater Simulation in Floodplain Areas: A Case Study of Irtysh River, China. *Water*. 2023; 15(17):3059.
https://doi.org/10.3390/w15173059

**Chicago/Turabian Style**

Liu, Yin, Yunzhong Jiang, Shuanghu Zhang, Dan Wang, and Huan Chen.
2023. "Application of a Linked Hydrodynamic–Groundwater Model for Accurate Groundwater Simulation in Floodplain Areas: A Case Study of Irtysh River, China" *Water* 15, no. 17: 3059.
https://doi.org/10.3390/w15173059