# A Hybrid Coupled Model for Groundwater-Level Simulation and Prediction: A Case Study of Yancheng City in Eastern China

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## Abstract

**:**

## 1. Introduction

^{2}. The largest settlement center is located at Dafeng Haifeng Farm in Yancheng City, and the cumulative land subsidence is more than 700 mm.

## 2. Study Area and Methods

#### 2.1. Overview of the Study Area

^{2}. The geographical location is shown in Figure 1. The study area is densely networked with water and meanders, and belongs to the coastal water network plain landform type. The topography of the study area is flat, with a general trend of high elevation in the southeast and low elevation in the northwest. The topography of the area is flat and slopes slowly from southeast to northwest.

#### 2.2. Data Analysis and Modeling Process

#### 2.2.1. Spatiotemporal Data Analysis

- (1)
- Skewness coefficients, kurtosis coefficients, and non-parametric tests were used to determine whether the data were normally distributed. Analysis was performed using SPSS software(Version 21.0), and when the sample content n ≤ 2000, the results were based on the Shapiro–Wilk (W-test); when the sample content n > 2000, the results were based on the Kolmogorov–Smirnov (D-test). For unweighted or integer weights, the Shapiro–Wilk statistic was calculated when the weighted sample size was between 3 and 5000, while for single samples, the Kolmogorov–Smirnov test can be used to test whether the variables are normally distributed.
- (2)
- Time stationarity test [57]. This paper used the spatial trend analysis tool in ArcGIS to analyze the groundwater dynamic monitoring data in the study area as a trend surface to test the spatial smoothness; the test of temporal smoothness is mainly achieved through time series analysis. Time series analysis means that the time series is regarded as a random process that does not vary with time [58]. For a time series ${z}_{i}\left(t\right)$, the expression for the mean is$${u}_{{z}_{i}(t)}=\frac{\sum _{i}^{N}\sum _{t}^{T}{z}_{i}\left(t\right)}{NT}(i=1,\dots ,N;t=1,\dots ,T)$$

- (3)
- Spatial variability analysis uses semi-variance functions to analyze spatial data. The semi-variance function $r(h)$, also known as the semi-variance function, is expressed as half of the variable between ${z}_{i}$ at points i and i + h and ${z}_{i+h}$ with the expression$$r(h)=\frac{1}{2N(h)}{\sum}_{i=1}^{N(h)}{({z}_{i}-{z}_{i+h})}^{2}$$

#### 2.2.2. STARMA Modeling

- (1)
- The identification of the model is based on the truncated or trailing nature of its space–time autocorrelation function (STACF) and space–time partial autocorrelation function (STPACF). In this paper, based on the autocorrelation and bias correlation coefficients on the spatiotemporal data, the model chosen was identified as the spatiotemporal autocorrelation model STAR (2), with the specific expression$$z\left(t\right)={\phi}_{10}z(t-1)+{\phi}_{20}(t-2)+{\phi}_{11}{W}^{\left(1\right)}z(t-1)+{\phi}_{21}{W}^{\left(1\right)}z(t-2)+\epsilon (t)$$
- (2)
- Estimation of the parameters in the model is carried out using the least-squares and greatest likelihood methods. That is, in order to make the model output value as close as possible to the actual monitoring value, the sum of squares of the error between the model output value and the actual monitoring value are used to measure, and the parameter value with the smallest sum of squares is the parameter value of the model.
- (3)
- Model validation. The residual sequence of the model is tested to determine whether it is a random error. If the residual of the model is random error—that is, the mean and auto-covariance of the model residual are 0, and the variance is σ
^{2}—then the model is reasonable; otherwise, the selected model is unreasonable, which means that there is a certain pattern in the residual sequence—that is, there is a certain correlation or variability in space–time. If the selected model is unreasonable, it means that there is still some important information in the original space–time sequence that has not been extracted, and then the model and parameter estimation need to be re-selected.

#### 2.2.3. BP Neural Network Model Building

#### 2.2.4. BP-STARMA Model Building

## 3. Results and Discussion

#### 3.1. Data Processing and Analysis

#### 3.1.1. Monitoring Data Processing

#### 3.1.2. Data Analysis

_{0.05}= 1.96, which is tentatively considered not to conform to a normal distribution.

#### 3.2. BP-STARMA Model Building

#### 3.2.1. BP Neural Network to Extract Nonlinear Spatiotemporal Trends

#### 3.2.2. STARMA Modeling

^{−1}(N = 23 indicates the number of spatial cells, T = 32 indicates the number of groundwater level monitoring periods, and s = 2 indicates the time delay), this indicates that the spatiotemporal autocorrelation function values are close to random errors. The values of the spatiotemporal autocorrelation coefficients calculated for the residuals of the model are shown in the Table 6 below.

#### 3.3. Comparison of Model Prediction Accuracy

#### 3.4. Evaluation and Comparison of Comprehensive Model Performance

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Geographical location map of the study area. (

**a**) Jiangsu Province, China; (

**b**) Yancheng City; (

**c**) spatial location of boreholes in the study area.

**Figure 2.**Hydrogeological profile of the study area [55].

**Figure 4.**(

**a**) Diagram of the average water level variation of confined aquifer III; (

**b**) diagram of water level variation of different monitoring wells of confined aquifer III.

**Figure 5.**Autocorrelation function of mean groundwater table. Red dots represent the time autocorrelation function value of the groundwater level.

**Figure 6.**(

**a**) Spatiotemporal trend map extracted by BP neural network; (

**b**) Average groundwater level of the 10th, 20th, and 30th periods.

**Figure 7.**Comparison of predicted values and actual verification data of different models in different monitoring periods. (

**a**) Groundwater level elevation map fitted by BP-STARMA model; (

**b**) groundwater level elevation map fitted by STARMA model; (

**c**) groundwater level elevation map fitted by BP neural network model; (

**d**) groundwater level elevation map fitted by actual monitoring values.

**Figure 8.**Groundwater fitting and predicted change curves for different models at different monitoring wells.

Monitoring Well Number | Bias u | Peak State u |
---|---|---|

51073006# | 3.075023 | 0.559089 |

51073509# | 3.136233 | 0.852506 |

51073512# | 2.765471 | 1.891852 |

51074507# | 2.712559 | 0.273745 |

51073006# | 51073509# | 51073512# | 51074507# | ||
---|---|---|---|---|---|

N | 40 | 40 | 40 | 40 | |

Normal | Mean | −30.8653 | −19.5038 | −7.69125 | −36.1275 |

Parameters ^{a,b} | Std. Deviation | 2.783878 | 2.366837 | 0.55931 | 3.325536 |

Most Extreme Differences | Absolute | 0.320592 | 0.195934 | 0.159134 | 0.166015 |

Positive | 0.320592 | 0.195934 | 0.159134 | 0.166015 | |

Negative | −0.17658 | −0.10716 | −0.08156 | −0.15888 | |

Test Statistic | 0.320592 | 0.195934 | 0.159134 | 0.166015 | |

Asymp. Sig. (2-tailed) | 0.000 ^{c} | 0.000 ^{c} | 0.012 ^{c} | 0.007 ^{c} |

Number of Issues | Water Level (m) | Number of Issues | Water Level (m) | Number of Issues | Water Level (m) | Number of Issues | Water Level (m) |
---|---|---|---|---|---|---|---|

1 | −22.322 | 11 | −23.344 | 21 | −25.103 | 31 | −25.977 |

2 | −22.161 | 12 | −23.540 | 22 | −25.182 | 32 | −26.212 |

3 | −22.323 | 13 | −24.108 | 23 | −25.285 | 33 | −26.154 |

4 | −22.492 | 14 | −24.138 | 24 | −25.327 | 34 | −25.336 |

5 | −22.468 | 15 | −24.268 | 25 | −25.345 | 35 | −26.486 |

6 | −22.726 | 16 | −24.574 | 26 | −25.461 | 36 | −26.536 |

7 | −22.556 | 17 | −24.646 | 27 | −25.751 | 37 | −26.553 |

8 | −22.879 | 18 | −24.744 | 28 | −25.810 | 38 | −26.621 |

9 | −22.833 | 19 | −24.971 | 29 | −25.698 | 39 | −26.703 |

10 | −22.338 | 20 | −25.090 | 30 | −25.810 | 40 | −26.844 |

Number of Issues | Variable Range (km) | Offset Abutment Value (C) | Nugget Value (C_{0}) | Abutment Values (C _{0} + C) | C_{0}/Sill (%) |
---|---|---|---|---|---|

4 | 21.7 | 18.42 | 4.99 | 23.41 | 21.32 |

8 | 20.7 | 16.24 | 5.21 | 21.45 | 24.29 |

12 | 22.8 | 15.32 | 7.73 | 23.05 | 33.54 |

16 | 21.4 | 16.42 | 10.83 | 27.25 | 39.74 |

20 | 21.8 | 14.77 | 10.88 | 25.65 | 42.42 |

24 | 21.3 | 18.63 | 9.94 | 28.57 | 34.79 |

28 | 21.5 | 13.19 | 12.71 | 25.9 | 49.07 |

Coefficient | Std. | t-Statistic | Prob | |
---|---|---|---|---|

${\phi}_{10}$ | 0.54276 | 0.06895 | 4.5148 | 0.0132 |

${\phi}_{20}$ | 0.15267 | 0.07429 | 6.8419 | 0.0051 |

${\phi}_{11}$ | −0.38156 | 0.06472 | 6.7513 | 0.0024 |

${\phi}_{21}$ | 0.24158 | 0.05719 | 3.4856 | 0.0084 |

Space Delay (h) Time Delay (k) | 0 | 1 | Space Delay (h) Time Delay (k) | 0 | 1 |
---|---|---|---|---|---|

1 | 0.038 | −0.073 | 9 | 0.064 | −0.042 |

2 | −0.012 | −0.028 | 10 | 0.013 | 0.026 |

3 | 0.048 | −0.035 | 11 | −0.016 | −0.092 |

4 | −0.04 | −0.023 | 12 | 0.068 | −0.0011 |

5 | −0.03 | 0.017 | 13 | −0.0093 | 0.0017 |

6 | −0.027 | −0.021 | 14 | −0.037 | 0.061 |

7 | −0.034 | 0.019 | 15 | 0.0061 | −0.0347 |

8 | 0.017 | −0.068 | 16 | −0.015 | 0.0015 |

Periods | Fitted Values | Periods | Predicted Values | ||||
---|---|---|---|---|---|---|---|

RMSE | RMSE | ||||||

BP-STARMA | STARMA | BP | BP-STARMA | STARMA | BP | ||

10 | 0.662993 | 0.684267 | 0.630171 | 34 | 1.104 | 1.25 | 1.34 |

20 | 0.397683 | 0.536424 | 0.493816 | 37 | 1.38 | 1.1642 | 1.91 |

30 | 0.369923 | 0.361022 | 0.399997 | 40 | 2.20 | 2.718 | 2.69 |

Indicators | Models | 51072002# | 51072010# | 51073003# | 51073010# | 51074004# | 51074515# |
---|---|---|---|---|---|---|---|

RSE | BP-STARMA | 0.150101 | 0.283151 | 0.016342 | 0.220120 | 0.053888 | 0.303071 |

STARMA | 0.604417 | 0.904445 | 0.114733 | 0.049426 | 0.117395 | 0.53618 | |

BP | 0.828549 | 0.427072 | 0.022214 | 0.449457 | 0.399316 | 0.394206 | |

NMSE | BP-STARMA | 0.000254 | 0.000119 | 0.000381 | 0.000630 | 0.000205 | 0.000128 |

STARMA | 0.001012 | 0.000278 | 0.001797 | 0.000105 | 0.000448 | 0.000226 | |

BP | 0.00199 | 0.000247 | 0.000525 | 0.001161 | 0.000851 | 0.000239 | |

RMSE | BP-STARMA | 0.385879 | 0.347153 | 0.425131 | 0.704296 | 0.393573 | 0.370956 |

STARMA | 0.774334 | 0.620444 | 1.126466 | 0.333735 | 0.580906 | 0.493408 | |

BP | 1.0878 | 0.587649 | 0.500338 | 0.957361 | 0.798729 | 0.507498 | |

MAE | BP-STARMA | 0.315065 | 0.263823 | 0.339018 | 0.58108 | 0.27274 | 0.291155 |

STARMA | 0.619108 | 0.493683 | 0.767228 | 0.244518 | 0.44759 | 0.408922 | |

BP | 0.6692 | 0.449455 | 0.388958 | 0.627958 | 0.56586 | 0.377935 |

Monitoring Well Number | Fitted Values | Predicted Values | ||||
---|---|---|---|---|---|---|

RMSE | RMSE | |||||

BP-STARMA | STARMA | BP | BP-STARMA | STARMA | BP | |

51072002# | 0.3955 | 0.6583 | 0.5089 | 0.3448 | 1.1245 | 2.2092 |

51072010# | 0.3814 | 0.6187 | 0.4180 | 0.1440 | 0.3957 | 1.0137 |

51073003# | 0.3177 | 0.4555 | 0.3779 | 0.7070 | 2.3483 | 0.8249 |

51073010# | 0.5780 | 0.2346 | 0.4510 | 1.0695 | 0.5803 | 1.9414 |

51074004# | 0.2968 | 0.4336 | 0.4152 | 0.6497 | 0.9670 | 1.5812 |

51074515# | 0.3648 | 0.4221 | 0.3817 | 0.3745 | 0.7104 | 0.8396 |

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## Share and Cite

**MDPI and ACS Style**

Hou, M.; Chen, S.; Chen, X.; He, L.; He, Z.
A Hybrid Coupled Model for Groundwater-Level Simulation and Prediction: A Case Study of Yancheng City in Eastern China. *Water* **2023**, *15*, 1085.
https://doi.org/10.3390/w15061085

**AMA Style**

Hou M, Chen S, Chen X, He L, He Z.
A Hybrid Coupled Model for Groundwater-Level Simulation and Prediction: A Case Study of Yancheng City in Eastern China. *Water*. 2023; 15(6):1085.
https://doi.org/10.3390/w15061085

**Chicago/Turabian Style**

Hou, Manqing, Suozhong Chen, Xinru Chen, Liang He, and Zhichao He.
2023. "A Hybrid Coupled Model for Groundwater-Level Simulation and Prediction: A Case Study of Yancheng City in Eastern China" *Water* 15, no. 6: 1085.
https://doi.org/10.3390/w15061085