# Modeling and Investigating the Mechanisms of Groundwater Level Variation in the Jhuoshui River Basin of Central Taiwan

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Pearson Correlation Coefficient

_{i}and g

_{i}, where i = 1, 2, …, n), the correlation coefficient can estimate the Pearson correlation (R) between P and G. The calculation of the correlation coefficient is given as:

#### 2.2. Gamma Test (GT)

_{1}, …, x

_{m}), y), where X is the input items and scalar y is the output items, the observations can be described as Equation (2).

_{i}∈ R

^{m}are the m-dimensional input variables with a dataset length of M, which is constrained to a closed bounded set C ∈ R

^{m}. The corresponding outputs y

_{i}∈ R are scalars. The underlying relationship of the data set can be denoted:

_{i,k}denote the kth nearest neighbor to X

_{i}in terms of Euclidean distance. The delta function is defined:

#### 2.3. Back-Propagation Neural Network (BPNN)

#### 2.4. Adaptive Neuro-Fuzzy Inference System (ANFIS)

- Rule 1: If p is A
_{1}and s is B_{1}then g_{1}= k_{1}*p + t_{1}*s + r_{1} - Rule 2: If p is A
_{2}and s is B_{2}then g_{2}= k_{2}*p + t_{2}*s + r_{2}

## 3. Case Study

^{2}. Figure 3a shows the distribution of the gauge stations and the hydrogeological information of groundwater monitoring wells in the study area. There are 2 main regions in this study area: The mountain area and the alluvial fan. The alluvial fan can be roughly divided into 3 districts: The fan-top district; the fan-mid district; the fan-tail district (Figure 3a). The G1~G4 monitoring wells belong to the mountain area, and the G5~G8 monitoring wells belong to the fan-top of the alluvial fan. As shown in Figure 3b, the fan-top district is the only district without a significant confined aquifer. In general, the hydrogeological feature of the fan-top district in this study area is recognized as a high potential groundwater recharge area because the main geological components are sandstone, phyllite and slate (the gravel of the geological structure) (Figure 3b). According to investigations of core drilling samples, the soil thickness of this study area (the depth to bedrock, including the soil layer, colluvium layer and saprolite) is deep [32]. The Central Geological Survey (CGS) (Ministry of Economic Affairs (MOEA), R.O.C.) indicated that the hydrogeological structure of the study area can be divided into several strata. Based on the depth from the land surface (Figure 3b), these strata are as follows: Aquifer 1 (F1), Aquitard 1 (T1), Aquifer 2 (F2), Aquitard 2 (T2) and Aquifer 3 (F3). The average thicknesses of Aquifer 1, Aquifer 2 and Aquifer 3 are 42 m, 95 m and 86 m, respectively. The thickness of the gravel and sand strata in the fan-top areas can reach more than 130 m [33]. In this study area, some groundwater monitoring wells include two different depth monitoring records (in a different aquifer), such as G1, G4, G7 and G8 (Figure 3c). However, according the hydrogeological information provided by the CGS (Figure 3b), it is recognized that the shallow groundwater well in G7 belongs to Aquifer 3 (F3). The rainfall is distributed unevenly, which mainly occurs from May to September due to the unique topographical terrain and location. The total rainfall in wet periods comprises 75% of the annual rainfall, which implies rainfall differs significantly between wet and dry periods.

_{i}is the model estimation and d

_{i}is the observation, and N is the number of datasets. The RMSE is used to evaluate the accuracy of the estimations of the groundwater level variations. The lower the RMSE value is, the better is the model’s performance.

## 4. Results and Discussion

#### 4.1. Duration of Accumulated Rainfall Analysis

#### 4.2. Effective Rainfall Analysis

#### 4.3. Estimation of Groundwater Level Variations

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The distribution of the gauge stations and hydrogeological information of the groundwater monitoring wells.

**Figure 5.**Time series of the groundwater level at the groundwater monitoring wells and the rainfall data at R2.

**Figure 6.**The correlation coefficient between the groundwater level variation and rainfall durations at different groundwater monitoring wells.

**Figure 7.**The correlation between the groundwater level variations and the accumulated rainfall amount at different low thresholds (Lower bound screening).

**Figure 8.**The correlation between the groundwater level variations and the accumulated rainfall amount at different up thresholds (Upper bound screening).

Rainfall Station | Elevation (m) | Rainfall (mm) | ||
---|---|---|---|---|

Mean | SD ^{1} | Annual Rainfall | ||

R1 | 400 | 8.18 | 29.16 | 2985 |

R2 | 231 | 8.43 | 30.64 | 3076 |

R3 | 203 | 6.24 | 20.77 | 2278 |

R4 | 215 | 6.35 | 21.33 | 2320 |

R5 | 296 | 5.93 | 22.96 | 2166 |

R6 | 393 | 5.76 | 20.99 | 2103 |

R7 | 724 | 8.14 | 37.45 | 2970 |

R8 | 322 | 5.64 | 21.60 | 2059 |

R9 | 1666 | 7.31 | 26.50 | 2669 |

R10 | 485 | 8.91 | 29.34 | 3250 |

R11 | 2200 | 7.84 | 30.56 | 2863 |

R12 | 1135 | 6.04 | 25.60 | 2203 |

R13 | 1200 | 7.38 | 26.33 | 2695 |

R14 | 1520 | 7.01 | 27.07 | 2558 |

R15 | 2303 | 5.46 | 22.40 | 1991 |

R16 | 82 | 5.15 | 19.30 | 1880 |

R17 | 110 | 4.44 | 18.33 | 1620 |

^{1}Standard deviation.

Monitoring Well | Well Depth (m) | Elevation (m) | Groundwater Level (m) | |
---|---|---|---|---|

Mean | SD | |||

G1(1) [shallow] | 102.6 | 151.2 | 141.7 | 1.86 |

G1(2) [deep] | 199.3 | 151.2 | 142.7 | 1.46 |

G2 | 150 | 113.3 | 109.0 | 4.63 |

G3 | 24.1 | 179.3 | 169.1 | 1.03 |

G4(1) [shallow] | 78.2 | 151.1 | 137.6 | 2.17 |

G4(2) [deep] | 193.2 | 151 | 135.5 | 1.45 |

G5 | 112.7 | 82.4 | 38.75 | 3.35 |

G6 | 96 | 72.3 | 38.48 | 2.84 |

G7(1) [shallow] | 140 | 49.5 | 35.97 | 2.38 |

G7(2) [deep] | 269 | 49.6 | 34.02 | 2.31 |

G8(1) [shallow] | 38.7 | 46.6 | 34.73 | 1.55 |

G8(2) [deep] | 97.5 | 46.5 | 34.73 | 1.52 |

Stream Flow Station | Elevation (m) | Discharge (cm s) | |
---|---|---|---|

Mean | SD | ||

S1 | 107.17 | 136.51 | 401.22 |

S2 | 279.09 | 113.59 | 272.19 |

Groundwater Monitoring Well | Input Type: Streamflow | Input Type: Rainfall | Number of Datasets | |||
---|---|---|---|---|---|---|

Rainfall Duration (days) | Rainfall Gauging Station Selected | Average Rainfall (mm) | Standard Deviation (mm) | |||

G1(1) | S1; S2 | three | R2; R4 | 130 | 141 | 236 |

G1(2) | S1; S2 | four | R3; R13 | 146 | 152 | 169 |

G2 | S1; S2 | two | R3; R6 | 60 | 79 | 372 |

G3 | S1; S2 | three | R3 | 102 | 98 | 243 |

G4(1) | S1; S2 | two | R4; R7; R9 | 88 | 134 | 312 |

G4(2) | S1; S2 | two | R7; R9; R13 | 88 | 135 | 364 |

G5 | S1 | two | R4; R12 | 64 | 94 | 251 |

G6 | S1 | two | R3; R12 | 62 | 93 | 330 |

G7(1) | S1 | four | R17 | 145 | 120 | 139 |

G7(2) | four | R6; R7 | 171 | 252 | 154 | |

G8(1) | S1 | four | R17 | 139 | 120 | 142 |

G8(2) | S1 | four | R17 | 138 | 119 | 150 |

Well | ANN Model: BPNN ^{1} ANFIS ^{2} | RMSE (m) | Correlation Coefficient | ||||
---|---|---|---|---|---|---|---|

Training | Validation | Testing | Training | Validation | Testing | ||

G1(1) | BPNN (4-3-1) | 0.091 | 0.108 | 0.11 | 0.844 | 0.696 | 0.724 |

ANFIS (4-2-1) | 0.085 | 0.112 | 0.133 | 0.867 | 0.666 | 0.578 | |

G1(2) | BPNN (4-4-1) | 0.115 | 0.137 | 0.149 | 0.481 | 0.304 | 0.221 |

ANFIS (4-2-1) | 0.114 | 0.138 | 0.149 | 0.491 | 0.275 | 0.22 | |

G2 | BPNN (4-4-1) | 0.055 | 0.091 | 0.112 | 0.342 | 0.394 | 0.274 |

ANFIS (4-2-1) | 0.056 | 0.092 | 0.115 | 0.308 | 0.312 | 0.121 | |

G3 | BPNN (3-6-1) | 0.058 | 0.083 | 0.128 | 0.844 | 0.846 | 0.682 |

ANFIS (3-2-1) | 0.063 | 0.107 | 0.129 | 0.806 | 0.753 | 0.667 | |

G4(1) | BPNN (5-9-1) | 0.063 | 0.089 | 0.109 | 0.895 | 0.806 | 0.893 |

ANFIS (5-3-1) | 0.058 | 0.094 | 0.144 | 0.912 | 0.779 | 0.775 | |

G4(2) | BPNN (5-10-1) | 0.048 | 0.067 | 0.069 | 0.928 | 0.88 | 0.865 |

ANFIS (5-2-1) | 0.045 | 0.064 | 0.062 | 0.938 | 0.887 | 0.89 | |

G5 | BPNN (3-3-1) | 0.077 | 0.084 | 0.164 | 0.522 | 0.407 | 0.355 |

ANFIS (3-2-1) | 0.076 | 0.086 | 0.168 | 0.541 | 0.365 | 0.289 | |

G6 | BPNN (3-3-1) | 0.06 | 0.079 | 0.126 | 0.438 | 0.368 | 0.167 |

ANFIS (3-3-1) | 0.049 | 0.065 | 0.124 | 0.677 | 0.705 | 0.236 | |

G7(1) | BPNN (2-3-1) | 0.12 | 0.121 | 0.138 | 0.752 | 0.715 | 0.734 |

ANFIS (2-3-1) | 0.076 | 0.126 | 0.147 | 0.907 | 0.703 | 0.662 | |

G7(2) | BPNN (2-2-1) | 0.132 | 0.186 | 0.186 | 0.619 | 0.625 | 0.582 |

ANFIS (2-2-1) | 0.124 | 0.192 | 0.213 | 0.675 | 0.599 | 0.504 | |

G8(1) | BPNN (2-3-1) | 0.093 | 0.096 | 0.146 | 0.847 | 0.843 | 0.841 |

ANFIS (2-3-1) | 0.055 | 0.121 | 0.207 | 0.949 | 0.692 | 0.841 | |

G8(2) | BPNN (2-3-1) | 0.103 | 0.112 | 0.118 | 0.874 | 0.859 | 0.832 |

ANFIS (2-2-1) | 0.07 | 0.122 | 0.126 | 0.944 | 0.841 | 0.909 |

^{1}(number of input-number of nodes in the hidden layer-number of output);

^{2}(number of input-number of rules-number of output).

Well | Statistics (m) | |||
---|---|---|---|---|

Mean | SD | Maximum | Minimum | |

G1(1) | 0.15 | 0.19 | 1.19 | 0.01 |

G1(2) | 0.08 | 0.11 | 0.76 | 0.01 |

G2 | 0.16 | 0.65 | 7.95 | 0.01 |

G3 | 0.15 | 0.22 | 1.67 | 0.01 |

G4(1) | 0.27 | 0.45 | 2.78 | 0.01 |

G4(2) | 0.11 | 0.16 | 1.26 | 0.01 |

G5 | 0.07 | 0.1 | 0.86 | 0.01 |

G6 | 0.06 | 0.07 | 0.8 | 0 |

G7(1) | 0.06 | 0.07 | 0.37 | 0.01 |

G7(2) | 0.08 | 0.13 | 0.76 | 0.01 |

G8(1) | 0.08 | 0.09 | 0.45 | 0.01 |

G8(2) | 0.08 | 0.09 | 0.45 | 0.01 |

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## Share and Cite

**MDPI and ACS Style**

Bai, T.; Tsai, W.-P.; Chiang, Y.-M.; Chang, F.-J.; Chang, W.-Y.; Chang, L.-C.; Chang, K.-C.
Modeling and Investigating the Mechanisms of Groundwater Level Variation in the Jhuoshui River Basin of Central Taiwan. *Water* **2019**, *11*, 1554.
https://doi.org/10.3390/w11081554

**AMA Style**

Bai T, Tsai W-P, Chiang Y-M, Chang F-J, Chang W-Y, Chang L-C, Chang K-C.
Modeling and Investigating the Mechanisms of Groundwater Level Variation in the Jhuoshui River Basin of Central Taiwan. *Water*. 2019; 11(8):1554.
https://doi.org/10.3390/w11081554

**Chicago/Turabian Style**

Bai, Tao, Wen-Ping Tsai, Yen-Ming Chiang, Fi-John Chang, Wan-Yu Chang, Li-Chiu Chang, and Kuang-Chih Chang.
2019. "Modeling and Investigating the Mechanisms of Groundwater Level Variation in the Jhuoshui River Basin of Central Taiwan" *Water* 11, no. 8: 1554.
https://doi.org/10.3390/w11081554